Aptitude - Problems on H.C.F and L.C.M

Exercise :: Problems on H.C.F and L.C.M - General Questions

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

Answer: Option C

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

Answer: Option C

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

Answer: Option C

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

Answer: Option A

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

Answer: Option D

Explanation:

Required number = (L.C.M. of 12, 15, 20, 54) + 8

   = 540 + 8

   = 548.