# LCM Formula

The Least Common Multiple (LCM) 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 is the LCM of those two numbers. Check out the LCM formula for any two numbers and for fractions using GCD (HCF) in the table given below.

### Formula of L.C.M

Formulas To Calculate LCM
L.C.M formula for any two numbers L.C.M. =Â
$$\begin{array}{l}\frac{a\times b}{gcd\left(a,b\right)}\end{array}$$
LCM formula for Fractions L.C.M. =Â
$$\begin{array}{l}\frac{L.C.M\;of\;Numerator}{H.C.F\;of\;Denominator}\end{array}$$

It should be noted that the GCD or HCF is the greatest divisor which is divisible by both the numbers. Also, check the LCM of two numbersÂ to understand the steps to find the LCM of any two number easily.

### Solved Examples Using the L.C.M Formula

QuestionÂ 1: Find the LCM of (50, 65).

Solution:

The given number are (50, 65).

The numbers can be written in the form of their prime factors- 50 = 1

$$\begin{array}{l}\times\end{array}$$
2
$$\begin{array}{l}\times\end{array}$$
5
$$\begin{array}{l}\times\end{array}$$
5 65 = 1
$$\begin{array}{l}\times\end{array}$$
5
$$\begin{array}{l}\times\end{array}$$
13

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

Thus Least Common Multiple = (50

$$\begin{array}{l}\times\end{array}$$
65)/5 = 10
$$\begin{array}{l}\times\end{array}$$
65 = 650

Or,

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

$$\begin{array}{l}\times\end{array}$$
5
$$\begin{array}{l}\times\end{array}$$
5
$$\begin{array}{l}\times\end{array}$$
13 = 650

LCM (50, 65) = 650