HCF and LCM Practice Questions

Practice Questions on HCF and LCM

Q1. The HCF of two numbers is 8. Which of the following can never be their LCM?
a) 24 b) 48 c) 56 d) 60

Q2. The LCM of two numbers is 1820 and their HCF is 26. If one number is 130 then the other number is:
a) 70 b) 1690 c) 364 d) 1264

Q3. The HCF and LCM of two numbers are 11 and 385 respectively. The numbers are
a) 11 and 385 & 55 and 77 b) 55 and 77 c) 11 and 385 d) 22 and 770

Q4. If the ratio of two numbers is 2:3 and their LCM is 54, then the sum of the two numbers is
a) 5 b) 15 c) 45 d) 270

Q5. The sum of two numbers is 36 and their HCF is 4. How many pairs of such numbers are possible?
a) 1 b) 2 c) 3 d) 4

Q6. The HCF of two numbers, each having three digits is 17 and their LCM is 714. The sum of the numbers will be:
a) 289 b) 391 c) 221 d) 731

Q7. The HCF and product of two numbers are 15 and 6300 respectively. The number of positive pairs of the numbers is
a) 4 b) 3 c) 2 1)

Q8. The sum of two numbers is 384. HCF of the numbers is 48. The difference of the numbers is
a) 100 b) 192 c) 288 d) 336

Q9. The sum of two numbers is 36 and their HCF and LCM are 3 and 105 respectively. The sum of the reciprocals of two numbers is
a) 2/35 b) 3/25 c) 4/35 d) 2/25

Q10.The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils, is
a) 91 b) 910 c) 1001 d) 1911

Q11. Find the least multiple of 23, which when divided by 18,21 and 24 leaves the remainder 7, 10 and 13 respectively.
a) 3013 b) 3024 c) 3002 d) 3036

Q12. The greatest number, which when divided by 989 and 1327 leaves remainders 5 and 7 respectively is
a) 8 b) 16 c) 24 d) 32

Q13. Three numbers which are co prime to one another are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
a) 75 b) 81 c) 85 d) 89

Q14. Which is the least number of six digits which when divided by 4,6,10,15 leaves in each case same remainder 2 be N. The sum of digits in N is
a) 3 b) 5 c) 4 d) 6

Q15. A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7 is
a) 1539 b) 539 c) 359 d) 1359

Q16. What is the least number which when divided by the numbers 3,5,6,8,10 and 12 leaves in each case a remainder 2 but when divided by 13 leaves no remainder?
a) 312 b) 962 c) 1562 d) 1586

Q17. The greatest number of four digits which when divided by 12,16 and 24 leave remainders 2,6 and 14 respectively is
a) 9974 b) 9970 c) 9807 d) 9998

Q18.What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
a) 840 b) 841 c) 820 d) 814

Q19. From a point on a circular track 5 km long A, B and C started running in the same direction at the same time with speeds of 5/2 km per hour, 3 km per hour and 2 km per hour respectively. Then on the starting point all three will meet again after
a) 30 hours b) 6 hours c) 10 hours d) 15 hours

Q20. A farmer has 945 cows and 2475 sheep. He farms then into flocks, keeping cows and sheep separate and having the same number of animals in each flock. If these flocks are as large as possible, then the maximum number of animals in each flock and total number of flocks required for the purpose are respectively
a) 15 and 228 b) 9 and 380 c) 45 and 76 d) 46 and 75

Q21. The LCM of two numbers is 20 times their HCF. The sum of HCF and LCM is 2520. If one of the number is 480, the other number is
a) 400 b) 480 c) 520 d) 600

Answer Key

1d 2c 3a 4c 5c 6c 7c 8c 9c 10a 11a 12c 13c 14b 15c 16b 17a 18b 19c 20c 21d

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