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Problems on H.C.F and L.C.M Objective Questions and answer

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1.) Two numbers are in the ratio of 15:11. If their H.C.F. is 13, find the numbers.

A. 122 and 80                      B. 87 and 190

C. 195 and 143                    D. None of these

View Answer

Answer: Option C

Explanation:

Let the required numbers be 15.x and 11x.

Then, their H.C.F. is x. So, x = 13.

The numbers are (15 x 13 and 11 x 13) i.e., 195 and 143.


2.) The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers is 77,find the other.

A. 80                                 B. 57

C. 63                                 D. 99

View Answer

Answer: Option D
Explanation:
Other number = (11 X 693)/77   = 99


3.) Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.

A. 45 cm                            B. 57 cm

C. 63 cm                            D. 99 cm

View Answer

Answer: Option A
Explanation:

Required length = H.C.F. of 495 cm, 900 cm and 1665 cm.

495 = 32 x 5 x 11, 900 = 22 x 32 x 52, 1665 = 32 x 5 x 37.

binduH.C.F. = 32 x 5 = 45.

Hence, required length = 45 cm.


4.) Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case.

A. 35                                  B. 77

C. 73                                  D. 59

View Answer

Answer: Option A
Explanation:

Required number =  H.C.F. of (132 - 62), (237 - 132) and (237 - 62)

=  H.C.F. of 70, 105 and 175 = 35.


5.) Find the largest number of four digits exactly divisible by 12,15,18 and 27.

A. 5500                              B. 9000

C. 7300                              D. 9720

View Answer

Answer: Option D
Explanation:

The Largest number of four digits is 9999.

Required number must be divisible by L.C.M. of 12,15,18,27 i.e. 540.

On dividing 9999 by 540,we get 279 as remainder .

\Required number = (9999-279) = 9720.


 
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