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The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
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, 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 ?
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.
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015
Clearly, 252 = 2 x 2 x 3 x 3 x 7.
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