problems on hcf and lcm

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11. Find the lowest common multiple of 24, 36 and 40.
A. 120 B. 240
C. 360 D. 480

Answer: Option C

Explanation:

 

 2 | 24  -  36  - 40
 --------------------
 2 | 12  -  18  - 20
 --------------------
 2 |  6  -   9  - 10
 -------------------
 3 |  3  -   9  -  5
 -------------------
   |  1  -   3  -  5

L.C.M.  = 2 x 2 x 2 x 3 x 3 x 5 = 360.
12. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
A. 3 B. 13
C. 23 D. 33

Answer: Option C

Explanation:

 

L.C.M. of 5, 6, 4 and 3 = 60.

On dividing 2497 by 60, the remainder is 37.

Number to be added = (60 – 37) = 23.
13.
Reduce 128352 to its lowest terms.
238368
A.
3
4
B.
5
13
C.
7
13
D.
9
13

Answer: Option C

Explanation:

 

 128352) 238368 ( 1
         128352
         ---------------
         110016 ) 128352 ( 1
                  110016
                 ------------------  
                   18336 ) 110016 ( 6       
                           110016
                           -------
                                x
                           -------
 So, H.C.F. of 128352 and 238368 = 18336.

             128352     128352 ÷ 18336    7
 Therefore,  ------  =  -------------- =  --
             238368     238368 ÷ 18336    13
14. The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
A. 1677 B. 1683
C. 2523 D. 3363

Answer: Option B

Explanation:

 

L.C.M. of 5, 6, 7, 8 = 840.

Required number is of the form 840k + 3

Least value of k for which (840k + 3) is divisible by 9 is k = 2.

Required number = (840 x 2 + 3) = 1683.
15. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
A. 26 minutes and 18 seconds
B. 42 minutes and 36 seconds
C. 45 minutes
D. 46 minutes and 12 seconds

Answer: Option D

Explanation:

 

L.C.M. of 252, 308 and 198 = 2772.

So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.
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