Problems On Hcf And Lcm

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A:

9000

B:

9400

C:

9600

D:

9800

Answer: C

Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399.

Required number (9999 - 399) = 9600.

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Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

A:

4

B:

5

C:

6

D:

8

Answer: A

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

= H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

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Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

A:

4

B:

10

C:

15

D:

16

Answer: D

L.C.M. of 2, 4, 6, 8, 10, 12 is 120.

So, the bells will toll together after every 120 seconds(2 minutes).

In 30 minutes, they will toll together	30	+ 1 = 16 times.
	2

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The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

A:

276

B:

299

C:

322

D:

345

Answer: C

Clearly, the numbers are (23 x 13) and (23 x 14).

Larger number = (23 x 14) = 322.

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Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

A:

4

B:

7

C:

9

D:

13

Answer: A

Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)

= H.C.F. of 48, 92 and 140 = 4.

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Questions for: Problems On Hcf And Lcm