problems on hcf and lcm
12.  The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:  
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. 


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:  
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 ?  
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. 