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).


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 = \(\frac{50 \times 65}{5} = \frac{10}{65} = 65\)


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

Practise This Question

What direction must you swim at to cross the river in minimum time given the crocodiles have left and your maximum velocity is 5Kmhr and the velocity of river is 3Kmhr in the west direction.