# Method of L.C.M.

We will discuss here about the method of l.c.m. (least common multiple).

Let us consider the numbers 8, 12 and 16.

Multiples of 8 are → 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ......

Multiples of 12 are → 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, ......

Multiples of 16 are → 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176,  ......

The common multiple of 8, 12, 16 are 78, 96, ......

The least common multiple of 8, 12 and 16 is 48. (Smallest common multiple)

In short, the lowest common factor is expressed as L.C.M.

Finding L.C.M.

To find the L.C.M. we find prime factors of the given numbers.

Remember, we consider common prime factors only.

Example: Find the L.C.M. of 12, 16 and 24.

First we find the prime factors of the given numbers. 12 = 2 × 2 × 3

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 2 × 3

(2 comes maximum 4 times and 3 comes maximum once only.)

L.C.M. = 2 × 2 × 2 × 2 × 3

= 48 which is the product of their prime factors.

We can also find the L.C.M. of the given numbers by dividing all the numbers at the same time by a number that divides at least two of the given numbers. 1. When a number is not exactly divisible, we write the number itself below the line. 2. When we cannot divide the numbers by a common factor exactly we discontinue dividing the numbers.

L.C.M. = 2 × 2 × 2 × 3 × 2 = 48

Note:

The product of L.C.M. and H.C.F. of two numbers is also the product of the numbers.

For example, the L.C.M. of 7 and 14 is 14 and the H.C.F. of 7 and 14 = 7. We see that the product of 7 and 14 also the product of L.C.M. and H.C.F. of 7 and 14.