# 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 = 1255

65 = 1513

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

Thus Least Common Multiple =

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