What is the Least Common Multiple of 11520 and 11538?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 11520 and 11538 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 11520 and 11538, than apply into the LCM equation.

GCF(11520,11538) = 18
LCM(11520,11538) = ( 11520 × 11538) / 18
LCM(11520,11538) = 132917760 / 18
LCM(11520,11538) = 7384320

Least Common Multiple (LCM) of 11520 and 11538 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 11520 and 11538. First we will calculate the prime factors of 11520 and 11538.

Prime Factorization of 11520

Prime Factorization of 11538

Now multiplying the highest exponent prime factors to calculate the LCM of 11520 and 11538.

LCM(11520,11538) = 2⁸ × 3² × 5¹ × 641¹
LCM(11520,11538) = 7384320