HCF and LCM Competitive Exams
50 questions · Mathematics
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Question 1 of 50
Milk containers hold 403 L, 434 L and 465 L. The maximum capacity of a measure that can measure each quantity exactly is:
Explanation403 = 13×31, 434 = 14×31, 465 = 15×31, so HCF = 31.
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Question 2 of 50
Find the greatest 4-digit number divisible by 15, 25, 40 and 75.
ExplanationLCM = 600. 9999 ÷ 600 gives quotient 16, so the number is 600×16 = 9600.
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Question 3 of 50
The HCF of two numbers is 11 and their LCM is 693. If one number is 77, the other is:
ExplanationOther = (11×693) ÷ 77 = 99.
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Question 4 of 50
The product of the HCF and LCM of 24 and 36 is:
ExplanationHCF×LCM = product of the numbers = 24×36 = 864.
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Question 5 of 50
Find the smallest 4-digit number divisible by 12, 15, 20 and 27.
ExplanationLCM = 540. Smallest 4-digit multiple of 540 = 540×2 = 1080.
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Question 6 of 50
Boys can be arranged exactly in rows of 12, 18 or 24. The least number of boys is:
ExplanationLCM(12, 18, 24) = 72.
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Question 7 of 50
Three bells toll at intervals of 12, 15 and 20 seconds. If they toll together at the start, after how many minutes will they next toll together?
ExplanationLCM(12, 15, 20) = 60 seconds = 1 minute.
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Question 8 of 50
Find the LCM of 12, 18 and 24.
Explanation12 = 2²×3, 18 = 2×3², 24 = 2³×3, so LCM = 2³×3² = 72.
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Question 9 of 50
Find the HCF of 156 and 234.
Explanation156 = 2²×3×13 and 234 = 2×3²×13, so HCF = 2×3×13 = 78.
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Question 10 of 50
Find the HCF of 144, 180 and 252.
ExplanationCommon prime powers are 2² and 3², so HCF = 4×9 = 36.
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Question 11 of 50
Find the LCM of 2/3, 4/9 and 5/6.
ExplanationLCM of fractions = LCM of numerators ÷ HCF of denominators = 20 ÷ 3.
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Question 12 of 50
Find the LCM of the co-prime numbers 8 and 15.
ExplanationFor co-prime numbers LCM = product = 8×15 = 120.
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Question 13 of 50
The HCF of two consecutive natural numbers is:
ExplanationConsecutive numbers are co-prime, so their HCF is always 1.
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Question 14 of 50
Find the HCF of 1.2, 1.8 and 3.0.
ExplanationWrite as 12, 18, 30 (×0.1). HCF = 6, so the answer is 0.6.
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Question 15 of 50
The sum of two numbers is 36, their HCF is 4 and their LCM is 48. The sum of their reciprocals is:
ExplanationProduct = 4×48 = 192. Sum of reciprocals = (a+b)/ab = 36/192 = 3/16.
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Question 16 of 50
Three traffic lights change after every 48 s, 72 s and 108 s. If they change together at 8:00:00 am, they will next change together at:
ExplanationLCM(48, 72, 108) = 432 s = 7 min 12 s.
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Question 17 of 50
Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
ExplanationHCF(285−9, 1249−7) = HCF(276, 1242) = 138.
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Question 18 of 50
Two numbers are in the ratio 3 : 4 and their LCM is 120. Their sum is:
ExplanationNumbers are 3x and 4x, LCM = 12x = 120, so x = 10. Numbers are 30 and 40; sum = 70.
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Question 19 of 50
Find the LCM of 2/5, 4/15 and 6/25.
ExplanationLCM of numerators (2, 4, 6) = 12; HCF of denominators (5, 15, 25) = 5; so LCM = 12/5.
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Question 20 of 50
Three runners take 40 s, 60 s and 90 s to complete one round of a circular track. If they start together, they will meet again at the start after:
ExplanationLCM(40, 60, 90) = 360 s = 6 minutes.
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Question 21 of 50
Find the least number which when divided by 8, 12 and 15 leaves remainders 5, 9 and 12 respectively.
ExplanationEach divisor minus remainder is 3, so number = LCM − 3 = 120 − 3 = 117.
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Question 22 of 50
Three ropes of 42 m, 63 m and 84 m are cut into equal pieces of the greatest possible length. The length of each piece is:
ExplanationHCF(42, 63, 84) = 21 m. This gives 2 + 3 + 4 = 9 pieces.
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Question 23 of 50
The LCM of two numbers is 14 times their HCF. The sum of HCF and LCM is 600. If one number is 280, the other is:
ExplanationHCF + 14×HCF = 600 gives HCF = 40, LCM = 560. Other = (40×560) ÷ 280 = 80.
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Question 24 of 50
Find the largest number which divides 62, 132 and 237 leaving the same remainder in each case.
ExplanationHCF of the differences (70, 175) = 35. Remainder is 27 each time.
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Question 25 of 50
Find the least number which when divided by 12, 15, 20 and 54 leaves remainder 8 in each case.
ExplanationLCM = 540, so number = 540 + 8 = 548.
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Question 26 of 50
Find the LCM of 15, 20, 25 and 30.
ExplanationHighest powers: 2², 3 and 5², so LCM = 4×3×25 = 300.
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Question 27 of 50
Find the HCF of 2/3, 8/9, 16/81 and 10/27.
ExplanationHCF of fractions = HCF of numerators ÷ LCM of denominators = 2 ÷ 81.
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Question 28 of 50
Find the least number which when divided by 6, 9, 15 and 18 leaves remainder 4 in each case.
ExplanationLCM = 90, so number = 90 + 4 = 94.
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Question 29 of 50
The HCF of two numbers is 23 and the other factors of their LCM are 13 and 14. The larger number is:
ExplanationNumbers are 23×13 = 299 and 23×14 = 322. The larger is 322.
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Question 30 of 50
Find the HCF of 3/4, 9/16 and 15/32.
ExplanationHCF of numerators (3, 9, 15) = 3; LCM of denominators (4, 16, 32) = 32; so HCF = 3/32.
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Question 31 of 50
The product of two numbers is 2028 and their HCF is 13. Their LCM is:
ExplanationLCM = product ÷ HCF = 2028 ÷ 13 = 156.
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Question 32 of 50
Find the HCF of 1/2, 3/4 and 5/6.
ExplanationHCF of numerators (1, 3, 5) = 1; LCM of denominators (2, 4, 6) = 12; so HCF = 1/12.
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Question 33 of 50
Two numbers are in the ratio 2 : 3 and their HCF is 8. Their LCM is:
ExplanationNumbers are 16 and 24. LCM = 16×24 ÷ 8 = 48.
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Question 34 of 50
The HCF and LCM of two numbers are 12 and 240. If one number is 48, the other is:
ExplanationProduct of numbers = HCF×LCM, so other = (12×240)÷48 = 60.
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Question 35 of 50
Find the LCM of 0.6, 9.6 and 0.12.
ExplanationWrite as 60, 960 and 12 (×0.01). LCM = 960, so the answer is 9.60.
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Question 36 of 50
Find the least number which, when increased by 6, is exactly divisible by 24, 32, 36 and 54.
ExplanationLCM = 864, so number = 864 − 6 = 858.
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Question 37 of 50
Four bells toll at intervals of 12, 15, 20 and 30 seconds. After how many seconds will they toll together again?
ExplanationLCM(12, 15, 20, 30) = 60.
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Question 38 of 50
Find the HCF of 408 and 1032.
ExplanationEuclid: 1032 = 2×408 + 216; 408 = 1×216 + 192; 216 = 1×192 + 24; 192 = 8×24. HCF = 24.
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Question 39 of 50
Find the largest 3-digit number divisible by 6, 8 and 12.
ExplanationLCM = 24. Since 999 ÷ 24 gives quotient 41, the number is 24×41 = 984.
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Question 40 of 50
Buses leave a stand together at 6:00 am and then every 20, 25 and 30 minutes respectively. They will next leave together at:
ExplanationLCM(20, 25, 30) = 300 min = 5 hours, so 6:00 am + 5 h = 11:00 am.
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Question 41 of 50
A floor is 15 m 17 cm long and 9 m 2 cm wide. The side of the largest square tile that exactly covers it is:
ExplanationHCF(1517, 902) = 41 cm.
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Question 42 of 50
Find the LCM of 3/8, 9/16 and 15/32.
ExplanationLCM of numerators (3, 9, 15) = 45; HCF of denominators (8, 16, 32) = 8; so LCM = 45/8.
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Question 43 of 50
Find the largest number which divides 245 and 1029 leaving remainder 5 in each case.
ExplanationHCF(240, 1024) = 16.
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Question 44 of 50
Find the least number which leaves remainder 1 when divided by 5, 6, 8, 9 or 12 but is exactly divisible by 13.
ExplanationLCM = 360, so the number is 360k + 1. Testing k = 1, 2, … the first that is divisible by 13 is k = 10, giving 3601 = 13×277.
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Question 45 of 50
Find the LCM of 1.2 and 1.8.
ExplanationWrite as 12 and 18 (×0.1). LCM = 36, so the answer is 3.6.
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Question 46 of 50
Find the smallest 5-digit number divisible by 12, 18 and 21.
ExplanationLCM = 252. 10000 ÷ 252 gives about 39.7, so the next whole multiple is 252×40 = 10080.
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Question 47 of 50
Find the HCF of 36 and 84.
Explanation36 = 2²×3² and 84 = 2²×3×7, so HCF = 2²×3 = 12.
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Question 48 of 50
Find the greatest length of tape that can measure exactly 3 m 15 cm, 4 m 20 cm and 5 m 25 cm.
ExplanationHCF(315, 420, 525) = 105 cm.
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Question 49 of 50
Find the HCF of 0.63, 1.05 and 2.1.
ExplanationWrite as 63, 105, 210 (×0.01). HCF = 21, so the answer is 0.21.
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Question 50 of 50
Find the LCM of 16, 24, 36 and 54.
ExplanationHighest powers: 2⁴ and 3³, so LCM = 16×27 = 432.
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