# LCM Formula

The Least Common Multiple of two integers a and b, usually denoted by LCM (a, b), is the smallest positive integer that is divisible by both a and b. In simple words, the smallest positive number that is a multiple of two or more numbers.

L.C.M formula for any two numbers is,

$\large L.C.M=\frac{a\times b}{gcd\left(a,b\right)}$

LCM formula for \fraction is given by,

$\large L.C.M=\frac{L.C.M\;of\;Numerator}{H.C.F\;of\;Denominator}$

The GCD or HCF is the greatest divisor which is divisible by both the numbers.

### Solved Examples

Question 1: Find the LCM of (50, 65).

Solution:

Given number is (50, 65).

The numbers can be written in the form of their prime factors-

50 = 1$\times$2$\times$5$\times$5

65 = 1$\times$5$\times$13

The greatest common factors (gcf) 0f (50,65) is 5.

Thus Least Common Multiple = $\frac{50 \times 65}{5} = \frac{10}{65} = 65$

Or,

The primes common to both are 2, 5, 5, 13 .
Hence, the LCM of (50, 65) = 2 $\times$ 5 $\times$ 5 $\times$ 13 = 650

LCM (50, 65) = 650