# problems on hcf and lcm

21. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
 A. 15 cm B. 25 cm C. 35 cm D. 42 cm

Explanation:

Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.

22. Three numbers which are co-prime to each other 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

Explanation:

Since the numbers are co-prime, they contain only 1 as the common factor.

Also, the given two products have the middle number in common.

So, middle number = H.C.F. of 551 and 1073 = 29;

 First number = 551 = 19;    Third number = 1073 = 37. 29 29

Required sum = (19 + 29 + 37) = 85.

23. Find the highest common factor of 36 and 84.
 A. 4 B. 6 C. 12 D. 18

Explanation:

36 = 22 x 32

84 = 22 x 3 x 7

H.C.F. = 22 x 3 = 12.

24. Which of the following fraction is the largest ?
A.
 7 8
B.
 13 16
C.
 31 40
D.
 63 80

Explanation:

L.C.M. of 8, 16, 40 and 80 = 80.

 7 = 70 ; 13 = 65 ; 31 = 62 8 80 16 80 40 80

 Since, 70 > 65 > 63 > 62 , so 7 > 13 > 63 > 31 80 80 80 80 8 16 80 40

 So, 7 is the largest. 8

25. The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
 A. 504 B. 536 C. 544 D. 548