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# LCM & HCF 1. The LCM of two numbers is 864 and their HCF is 144. One of the numbers is 288, the other is:
(a) 576       (b) 432
(c) 1296     (d) 144

2. LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other will be:
(a) 5          (b) 25
(c) 45      (d) 55

3. The LCM of two numbers is 30 and their HCF is 5. One of the numbers is 10, the other is:
(a) 20        (b) 25
(c) 15       (d) 54

Q4. The HCF and LCM of two numbers are 13 and 455, respectively. If one of the numbers lies between 75 and 125, then, that number is:
(a) 78         (b) 91
(c) 104       (d) 117

Q5. The least number which when divided by 4, 6, 8, 12 and 16 leaves a remainder of 2 in each case is:
(a) 46         (b) 48
(c) 50       (d) 566

Q6. The least number, which when divided by 12, 15, 20 or 54 leaves a remainder of 4 in each case is:
(a) 450        (b) 454
(c) 540        (d) 544

Q7. The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets same number of pens and same number of pencils, is:
(a) 91           (b) 910
(c) 1001        (d) 1911

Q8. Four bells ring at intervals of 4, 6, 8 and 14 seconds. They start ringing simultaneously at 12 O’ clock. They will again ring simultaneously at:
(a) 12 hrs 2 min 48 sec         (b) 12 hrs 3 min 30 sec
(c) 12 hrs 3 min 20 sec               (d) 12 hrs 3 min 44 sec

Q9. The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers?
(a) 8 and 6        (b) 8 and 10
(c) 2 and 4        (d) 6 and 4

Q10. The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is:
(a) 10          (b) 46
(c) 70            (d) 90

Q11. Two numbers, both greater than 29, have HCF and LCM, 4147. The sum of the numbers is:
(a) 966         (b) 696
(c) 669         (d) 666

Q12. The HCF of two numbers is 8. Which one of the following can never be their LCM?
(a) 24           (b) 48
(c) 56           (d) 60

Q13. The LCM and the HCF of the numbers 28 and 42 are in the ratio:
(a) 6 : 1        (b) 2 : 3
(c) 3 : 2          (d) 7 : 2

Q14. The LCM of two numbers is 1820 and their HCF is 26. If one number is 130, the other is:
(a) 70           (b) 1690
(c) 364       (d) 1264

Q15. The LCM of two numbers is 1920 and their HCF is 16. If one of the numbers is 128, the other is:
(a) 204         (b) 240
(c) 260         (d) 320

Q16. The HCF of two numbers 12906 and 14818 is 478. Their LCM is:
(a) 400086         (b) 200043
(c) 600129             (d) 800172

Q17. Find the greatest number of five digits which when divided by 3, 5, 8, 12 leaves 2 as remainder
(a) 99990        (b) 99948
(c) 99962        (d) 99722

Q18. The least multiple of 13, which on dividing by 4,5,6,7 and 8 leaves remainder 2 in each case is:
(a) 2520          (b) 842
(c) 2522         (d) 840

Q19. Find the largest number of four digits such that on dividing by 15, 18, 21 and 24, the remainders are 11, 14, 17 and 20 respectively.
(a) 6557           (b) 7556
(c) 5675            (d) 7664

Q20. 4 bells ring at intervals of 30 minutes, 1 hour, 3/2 hour and 1 hour 45 minutes respectively. All the bells ring simultaneously at 12 noon. They will again ring at:
(a) 12 mid night       (b) 3 a.m.
(c) б a.m.                   (d) 9 p.m.