1. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The maximum number of columns in which they can march is:
(a) 4 (b) 6 (c) 8 (d) 12
Hint: Find the HCF of 616 and 32.
2. A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to stack them equally. What is the maximum number of barfis that can be placed in each stack?
(a) 10 (b) 20 (c) 30 (d) 5
Hint: Find the HCF of 420 and 130.
3. A merchant has three pieces of timber of lengths 42m, 49m, and 63m. The greatest possible length of equal planks that can be cut from them is:
(a) 9m (b) 7m (c) 14m (d) 21m
Hint: Find the HCF of 42, 49, and 63.
4. The maximum number of students among whom 1001 pens and 910 pencils can be distributed equally so that each student gets the same number of items is:
(a) 91 (b) 11 (c) 13 (d) 7
Hint: Find the HCF of 1001 and 910.
5. A rectangular courtyard is 18m 72cm long and 13m 20cm broad. The side of the largest square tile that can pave it exactly is:
(a) 12cm (b) 24cm (c) 36cm (d) 48cm
Hint: Find the HCF of 1872 and 1320.
6. Two tankers contain 850 litres and 680 litres of petrol. The maximum capacity of a container that can measure the petrol of either tanker exactly is:
(a) 17L (b) 170L (c) 340L (d) 20L
Hint: Find the HCF of 850 and 680.
7. A merchant has 120 litres of oil and 180 litres of ghee. The largest size of equal bottles required to store both without mixing is:
(a) 30L (b) 60L (c) 20L (d) 90L
Hint: Find the HCF of 120 and 180.
8. Find the longest tape which can be used to measure exactly the lengths 336 cm, 240 cm, and 96 cm:
(a) 48cm (b) 24cm (c) 12cm (d) 96cm
Hint: Calculate the HCF of 336, 240, and 96.
9. A stack of 144 cartons of Coke and 90 cartons of Pepsi are arranged equally. The maximum number of cartons possible in each equal stack is:
(a) 12 (b) 18 (c) 6 (d) 9
Hint: Find the HCF of 144 and 90.
10. A gardener has 44 apple trees and 66 banana trees. The maximum number of trees per row (if all rows must be equal) is:
(a) 11 (b) 22 (c) 4 (d) 6
Hint: Find the HCF of 44 and 66.
11. 105 goats and 175 cows are moved in equal groups. The maximum number of animals per group that can be taken in the boat is:
(a) 25 (b) 35 (c) 5 (d) 15
Hint: Find the HCF of 105 and 175.
12. Using the Fundamental Theorem of Arithmetic, the HCF of 135 and 225 is calculated as:
(a) 15 (b) 30 (c) 45 (d) 75
Hint: Find the greatest common prime factors.
13. Two rolls of wire are 140m and 160m. The greatest length of equal pieces into which they can be cut is:
(a) 10m (b) 20m (c) 40m (d) 5m
Hint: Find the HCF of 140 and 160.
14. 60 students of Class X and 84 students of Class XI are standing in equal rows. The maximum number of students per row is:
(a) 6 (b) 12 (c) 4 (d) 10
Hint: Find the HCF of 60 and 84.
15. The HCF of the smallest composite number and the smallest prime number is:
(a) 1 (b) 2 (c) 4 (d) 0
Hint: Numbers are 4 and 2. Find their HCF.
16. If two numbers are given as 18 and 24, their Highest Common Factor (HCF) is:
(a) 2 (b) 3 (c) 6 (d) 12
Hint: List common factors.
17. A tailor has cloth pieces of length 90cm and 120cm. The greatest length of strips he can cut equally from both is:
(a) 10cm (b) 20cm (c) 30cm (d) 15cm
Hint: Find the HCF of 90 and 120.
18. The HCF of 2³ × 3² and 2² × 3³ is:
(a) 2³ × 3³ (b) 2² × 3² (c) 2 × 3 (d) 2⁵ × 3⁵
Hint: Take the smallest power of common bases.
19. 72 boys and 90 girls are split into equal teams for a quiz. The maximum team size possible is:
(a) 9 (b) 18 (c) 8 (d) 12
Hint: Find the HCF of 72 and 90.
20. 120 Indian and 180 Foreign delegates are seated in equal rows. The maximum number of delegates per row is:
(a) 30 (b) 60 (c) 20 (d) 40
Hint: Find the HCF of 120 and 180.
21. The HCF of the three numbers 18, 24, and 30 is:
(a) 2 (b) 3 (c) 6 (d) 12
Hint: Find the greatest factor common to all three.
22. Determine the greatest length of a scale that can be used to measure exactly 24m, 32m, and 44m:
(a) 2m (b) 4m (c) 8m (d) 12m
Hint: Find the HCF of 24, 32, and 44.
23. A milkman has 45L and 75L of milk. The maximum capacity of a measuring jug that can empty both is:
(a) 5L (b) 15L (c) 25L (d) 10L
Hint: Find the HCF of 45 and 75.
24. If xᵃyᵇ and xᶜyᵈ are two terms where a < c and b > d, their HCF is:
(a) xᵃyᵈ (b) xᶜyᵇ (c) xᵃ⁺ᶜ yᵇ⁺ᵈ (d) xy
Hint: Use the lowest powers of common variables.
25. 48 students of Red House and 60 students of Blue House stand in equal rows. The maximum per row is:
(a) 6 (b) 12 (c) 8 (d) 4
Hint: Find the HCF of 48 and 60.
26. Three bells ring at intervals of 9, 12, and 15 minutes. If they ring together now, they will ring together again after:
(a) 60m (b) 120m (c) 180m (d) 90m
Hint: Find the LCM of 9, 12, and 15.
27. Sonia takes 18 minutes and Ravi takes 12 minutes to drive a lap. They will meet at the start again after:
(a) 6m (b) 30m (c) 36m (d) 48m
Hint: Find the LCM of 18 and 12.
28. Traffic lights at three crossings change every 48, 72, and 108 seconds. The simultaneous change interval is:
(a) 432s (b) 216s (c) 144s (d) 500s
Hint: Find the LCM of 48, 72, and 108.
29. The smallest number which is exactly divisible by both 28 and 32 is:
(a) 224 (b) 112 (c) 448 (d) 56
Hint: Calculate the LCM of 28 and 32.
30. Two electronic beepers beep every 60s and 62s. If they beep at 10 AM, they will beep together again after:
(a) 1860s (b) 3720s (c) 122s (d) 2s
Hint: Find the LCM of 60 and 62.
31. Hotdog buns are sold in packs of 8 and sausages in packs of 12. The least matching count needed to buy equal numbers is:
(a) 12 (b) 24 (c) 36 (d) 48
Hint: Find the LCM of 8 and 12.
32. Neon sign A flashes every 4s and Sign B flashes every 6s. Their next simultaneous flash occurs after:
(a) 10s (b) 12s (c) 24s (d) 2s
Hint: Find the LCM of 4 and 6.
33. Steps of three people measure 80cm, 85cm, and 90cm. The minimum distance they must walk to cover the same distance in complete steps is:
(a) 12240cm (b) 6120cm (c) 3060cm (d) 24480cm
Hint: Find the LCM of 80, 85, and 90.
34. The least number of plants required to be arranged in equal rows of 12, 15, or 18 is:
(a) 120 (b) 180 (c) 90 (d) 360
Hint: Find the LCM of 12, 15, and 18.
35. Two buses leave a depot every 20m and 30m. Their next common leave after 8:00 AM is at:
(a) 8:50 AM (b) 9:00 AM (c) 8:40 AM (d) 8:10 AM
Hint: Find the LCM of 20 and 30.
36. Three alarm clocks ring every 15, 30, and 45 minutes. Their synchronization time is:
(a) 90m (b) 45m (c) 135m (d) 60m
Hint: Find the LCM of 15, 30, and 45.
37. The smallest square area formed by tiles of size 20cm x 30cm has a side length of:
(a) 10cm (b) 50cm (c) 60cm (d) 120cm
Hint: The side length is the LCM of 20 and 30.
38. A radio jingle plays every 15m and an advertisement every 25m. They overlap every:
(a) 40m (b) 75m (c) 50m (d) 100m
Hint: Find the LCM of 15 and 25.
39. Two athletes lap in 40s and 50s. They meet at the starting point after:
(a) 100s (b) 200s (c) 400s (d) 10s
Hint: Find the LCM of 40 and 50.
40. The minimum number of books required for sections of 32 or 36 students to receive them equally is:
(a) 288 (b) 144 (c) 576 (d) 96
Hint: Find the LCM of 32 and 36.
41. Irrigation drip emitters drip water every 4s and 10s. They sync their drips every:
(a) 14s (b) 20s (c) 40s (d) 2s
Hint: Find the LCM of 4 and 10.
42. Ships sail from a port every 10 and 14 days. They will sail together again after:
(a) 24 days (b) 70 days (c) 140 days (d) 4 days
Hint: Find the LCM of 10 and 14.
43. Wheel circumferences are 40cm and 50cm. The least distance for both to complete full rotations is:
(a) 100cm (b) 200cm (c) 400cm (d) 10cm
Hint: Find the LCM of 40 and 50.
44. Two bells ring every 18m and 24m. If they ring together at 12 PM, they next ring together at:
(a) 12:42 PM (b) 1:12 PM (c) 1:24 PM (d) 12:36 PM
Hint: LCM is 72 minutes.
45. The least number of marbles that can be grouped into 10, 15, or 25 marbles without any leftover is:
(a) 150 (b) 300 (c) 75 (d) 50
Hint: Find the LCM of 10, 15, and 25.
46. Ferries arrive every 45m and 60m. Their next simultaneous arrival is after:
(a) 105m (b) 180m (c) 120m (d) 15m
Hint: Find the LCM of 45 and 60.
47. Gym sessions occur every 4 and 6 days. Two friends will meet again after:
(a) 10 days (b) 12 days (c) 24 days (d) 2 days
Hint: Find the LCM of 4 and 6.
48. A quick washer cycle is 40m and a heavy one is 50m. They finish together after:
(a) 90m (b) 200m (c) 100m (d) 10m
Hint: Find the LCM of 40 and 50.
49. Events A and B occur every 4 and 6 years. They coincide every:
(a) 10 years (b) 12 years (c) 24 years (d) 2 years
Hint: Find the LCM of 4 and 6.
50. Dance beats occur every 4 and 6 counts. They synchronize on beat number:
(a) 10 (b) 12 (c) 24 (d) 2
Hint: Find the LCM of 4 and 6.
51. The largest divisor of 2053 and 967 that leaves remainders 5 and 7 respectively is:
(a) 32 (b) 64 (c) 128 (d) 256
Hint: Find the HCF of 2048 and 960.
52. The least number which when divided by 35, 56, and 91 leaves a remainder of 7 in each case is:
(a) 3640 (b) 3647 (c) 3633 (d) 1827
Hint: Calculate the LCM(35, 56, 91) and add 7.
53. If the HCF(a, b) = 15 and the Product(a, b) = 1800, then the LCM is:
(a) 120 (b) 90 (c) 150 (d) 180
Hint: LCM = Product divided by HCF.
54. If LCM(x, 18) = 36 and HCF(x, 18) = 2, the value of x is:
(a) 2 (b) 3 (c) 4 (d) 1
Hint: Use the formula 18x = 72.
55. The greatest 4-digit number which is divisible by 15, 24, and 36 is:
(a) 9999 (b) 9720 (c) 9360 (d) 9000
Hint: LCM is 360; find the multiple near 9999.
56. The smallest 5-digit number divisible by 18, 24, and 30 is:
(a) 10000 (b) 10080 (c) 10800 (d) 10200
Hint: The LCM is 360; find the first 5-digit multiple.
57. The least number which when divided by 6, 7, 8, 9, and 12 leaves a remainder of 1 is:
(a) 505 (b) 504 (c) 253 (d) 1009
Hint: Calculate the LCM and add 1.
58. The product of the HCF and LCM of 12 and 18 is:
(a) 30 (b) 216 (c) 108 (d) 6
Hint: It is equal to 12 multiplied by 18.
59. Given HCF(26, 169) = 13, the LCM(26, 169) is:
(a) 26 (b) 169 (c) 338 (d) 13
Hint: Use the formula (26 × 169) / 13.
60. The least number divisible by each of the first 10 natural numbers is:
(a) 1260 (b) 2520 (c) 5040 (d) 100
Hint: Find the LCM of numbers 1 to 10.
61. The smallest number leaving a remainder of 3 when divided by 12, 15, and 18 is:
(a) 183 (b) 180 (c) 177 (d) 363
Hint: Find the LCM and add 3.
62. The largest divisor of 546 and 764 that leaves remainders of 6 and 8 is:
(a) 54 (b) 108 (c) 18 (d) 10
Hint: Find the HCF of 540 and 756.
63. The smallest 4-digit number divisible by 12, 15, 18, and 27 is:
(a) 1000 (b) 1080 (c) 1020 (d) 1100
Hint: The LCM of these numbers is 540.
64. The least number divided by 12, 16, 24, and 36 that leaves a remainder of 7 is:
(a) 151 (b) 144 (c) 79 (d) 137
Hint: Find the LCM and add 7.
65. The Highest Common Factor (HCF) of any two co-prime numbers is:
(a) 0 (b) 1 (c) Their product (d) None
Hint: Recall the definition of co-primes.
66. The least number which when increased by 15 is divisible by 15, 35, and 48 is:
(a) 1680 (b) 1665 (c) 1695 (d) 15
Hint: Find the LCM and subtract 15.
67. The least number which when decreased by 7 is divisible by 12, 16, 18, 21, and 28 is:
(a) 1008 (b) 1015 (c) 1001 (d) 7
Hint: Find the LCM and add 7.
68. The largest divisor of 398, 436, and 542 with remainders 7, 11, and 15 is:
(a) 17 (b) 11 (c) 13 (d) 7
Hint: Find the HCF of 391, 425, and 527.
69. The smallest number leaving remainders of 8 and 12 when divided by 28 and 32 is:
(a) 224 (b) 204 (c) 244 (d) 20
Hint: Use the formula LCM – (Divisor – Remainder).
70. The largest divisor of 245 and 1029 leaving a remainder of 5 is:
(a) 16 (b) 8 (c) 32 (d) 4
Hint: Find the HCF of 240 and 1024.
71. The value of the product HCF(p, q) × LCM(p, q) is always:
(a) p+q (b) p-q (c) p × q (d) p/q
Hint: This is the fundamental property of two numbers.
72. If the ratio of two numbers is 15:11 and their HCF is 13, the numbers are:
(a) 195, 143 (b) 150, 110 (c) 15, 11 (d) 130, 130
Hint: Multiply 15 and 11 by 13.
73. Is it possible for two numbers to have an HCF of 16 and an LCM of 380?
(a) Yes (b) No (c) Maybe (d) Data insufficient
Hint: Check if 380 is divisible by 16.
74. The number of distinct pairs of numbers with sum 528 and HCF 33 is:
(a) 4 (b) 8 (c) 1 (d) 16
Hint: Look for co-prime pairs (a,b) such that a+b = 16.
75. If the product of two numbers is 12960 and the HCF is 18, the LCM is:
(a) 720 (b) 360 (c) 180 (d) 1440
Hint: Divide the product by the HCF.
76. The least number of square tiles required for a room of 15m 17cm by 9m 2cm is:
(a) 814 (b) 41 (c) 414 (d) 1000
Hint: Tiles = Total Area divided by (HCF squared).
77. Bells sync every 180s. The number of times they sync in exactly 20 minutes is:
(a) 6 (b) 7 (c) 5 (d) 10
Hint: Divide 1200 seconds by 180.
78. For 120 Indians and 180 Foreigners, the total number of rooms needed (if per-room capacity is maximized) is:
(a) 60 (b) 5 (c) 2 (d) 3
Hint: Divide the total (300) by the HCF (60).
79. Runners A, B, and C take 6, 8, and 10 minutes respectively to complete one lap of a track. The number of laps completed by runner A when all first meet at the start is:
(a) 20 (b) 15 (c) 12 (d) 120
Hint: Divide the LCM(120) by 6.
80. For 945 cows and 2475 sheep, the total number of flocks (if per-flock size is maximized) is:
(a) 45 (b) 76 (c) 31 (d) 21
Hint: Divide the total count (3420) by 45.
81. Lights flash every 6, 9, 12s. The number of times they sync in exactly 1 hour is:
(a) 100 (b) 50 (c) 36 (d) 60
Hint: Divide 3600 by the LCM (36).
82. Stacks of 336, 240, and 96 books are made. The total number of stacks (if stack size is maximized) is:
(a) 48 (b) 14 (c) 7 (d) 2
Hint: Divide the total (672) by the HCF (48).
83. For rods measuring 64, 80, and 96cm, the usage count for the 64cm rod to measure the minimum possible cloth length is:
(a) 15 (b) 12 (c) 10 (d) 960
Hint: Divide the LCM(960) by 64.
84. In a hamper with 156, 208, and 260 items, the count of items in a single hamper (if hampers are maximized) is:
(a) 52 (b) 13 (c) 26 (d) 4
Hint: This is simply the HCF.
85. The minimum tower height reachable using blocks of 15cm and 25cm is:
(a) 40cm (b) 75cm (c) 150cm (d) 5cm
Hint: Find the LCM of 15 and 25.
86. If HCF(210, 55) = 210 × 5 + 55y, then the value of y is:
(a) -19 (b) 19 (c) 5 (d) -5
Hint: Solve the linear equation once you have the HCF.
87. The greatest 3-digit number divisible by 8, 10, and 12 is:
(a) 960 (b) 980 (c) 999 (d) 120
Hint: Find the largest multiple of 120.
88. The least number of soldiers in a parade with 15, 20, or 25 rows is:
(a) 300 (b) 600 (c) 150 (d) 75
Hint: Calculate the LCM.
89. The smallest number dividing by 12, 15, 20, 54 with a remainder of 8 is:
(a) 540 (b) 548 (c) 532 (d) 8
Hint: Find the LCM and add 8.
90. If LCM = 14 times HCF, and the sum is 600, with one number being 80, the other is:
(a) 280 (b) 40 (c) 560 (d) 600
Hint: HCF is 40 and LCM is 560.
91. The least square number divisible by 6, 9, 15, and 20 is:
(a) 180 (b) 900 (c) 3600 (d) 30
Hint: Adjust the LCM factors to form perfect squares.
92. On a 12km track with speeds of 3, 7, and 13 km/hr, runners will meet at the start after:
(a) 12h (b) 84h (c) 1h (d) 156h
Hint: Calculate the LCM of the fractional lap times.
93. The number of distinct pairs with sum 91 and HCF 7 is:
(a) 6 (b) 13 (c) 1 (d) 7
Hint: Look for co-prime pairs (a,b) where a+b = 13.
94. Given a ratio of 5:8 and a product of 12960, the numbers are:
(a) 90, 144 (b) 18, 144 (c) 45, 72 (d) 50, 80
Hint: Solve the equation 40x² = 12960.
95. If dividers 10, 9, 8 leave remainders 9, 8, 7, the smallest number is:
(a) 360 (b) 359 (c) 361 (d) 1
Hint: Use the LCM – 1 logic.
96. If dividers 24, 36, 48 leave remainders 21, 33, 45, the smallest number is:
(a) 144 (b) 141 (c) 147 (d) 3
Hint: Use the LCM – 3 logic.
97. If HCF(408, 1032) = 1032m – 2040, then the value of m is:
(a) 1 (b) 2 (c) 3 (d) 4
Hint: Equate 24 to the expression and solve.
98. The number of square tiles for a room of 1517cm by 902cm is:
(a) 814 (b) 41 (c) 33 (d) 100
Hint: Use total area divided by the square of HCF (41).
99. Given a sum of 105 and an LCM of 180, the two numbers are:
(a) 45, 60 (b) 30, 75 (c) 15, 90 (d) 50, 55
Hint: Use the HCF (15) and ratio logic.
100. The product of the HCF and LCM for the set {12, 15, 21} is:
(a) 1260 (b) 3780 (c) 420 (d) 3
Hint: Multiply 3 by the LCM (420).
