What is the Least Common Multiple of 13524 and 13538?

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 13524 and 13538 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13524 and 13538, than apply into the LCM equation.

GCF(13524,13538) = 14
LCM(13524,13538) = ( 13524 × 13538) / 14
LCM(13524,13538) = 183087912 / 14
LCM(13524,13538) = 13077708

Least Common Multiple (LCM) of 13524 and 13538 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13524 and 13538. First we will calculate the prime factors of 13524 and 13538.

Prime Factorization of 13524

Prime Factorization of 13538

Now multiplying the highest exponent prime factors to calculate the LCM of 13524 and 13538.

LCM(13524,13538) = 2² × 3¹ × 7² × 23¹ × 967¹
LCM(13524,13538) = 13077708