Least Common Multiple

Introduction:
   In arithmetic number of theory is the least common multiple or lowest common multiple (LCM) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both of a and of b. Since it was a multiple, it can be divided by a and b without a reminder. If either a or b is 0, so that number is no such positive integer, then LCM(a, b) is defined to be zero.

Example:

Multiples of 4 are
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, ......................
Multiple of 7 are
7, 14, 21, ................
(add 4 to each get to next multiple)

Applications

When adding and subtracting, or comparing vulgar fractions, Useful to find the least common multiple of the denominators, is  called the lowest common denominator. For instance,
{3\over15}+{1\over4}={12\over60}+{15\over60}={9\over20},
where the denominator of 60 was used to least common multiple of 15 and 4.

Hope you like the above explanation, Please leave your comments, if you have any doubts.