LOWEST COMMON MULTIPLE (L.C.M.)

The Lowest Common Multiple (L.C.M) is the smallest number that is a common multiple of two or more numbers.

For example, the L.C.M of 3 and 5 is 15 .(see the example above).

The simple method of finding the L.C.M of smaller numbers is to write down the multiples of the larger number until one of them is also a multiple of the smaller number.

Example 1:

Find the Lowest Common Multiple of 8 and 12.

Solution: Multiples of 12 are 12, 24...
24 is also a multiple of 8, so the L.C.M of 8 and 12 is 24.

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FINDING L.C.M. OF BIG NUMBERS

1. Find all the prime factors of both numbers.
2. Multiply all the prime factors of the larger number by those prime factors of the smaller number that are not already included.

Example:

Find the Lowest Common Multiple (L.C.M.) of 240 and 924.

From the example of finding the H.C.F. we know the prime factors of both numbers.

924 = 2 x 2 x 3 x 7 x 11
240 = 2 x 2 x 2 x 2 x 3 x 5

The L.C.M. is 2 x 2 x 3 x 7 x 11 x 2 x 2 x 5 = 924 x 20 = 18,480

Example 1



Example 2


Example 3



Example 4