What is the Least Common Multiple of 519 and 538?

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 519 and 538 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 519 and 538, than apply into the LCM equation.

GCF(519,538) = 1
LCM(519,538) = ( 519 × 538) / 1
LCM(519,538) = 279222 / 1
LCM(519,538) = 279222

Least Common Multiple (LCM) of 519 and 538 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 519 and 538. First we will calculate the prime factors of 519 and 538.

Prime Factorization of 519

Prime Factorization of 538

Now multiplying the highest exponent prime factors to calculate the LCM of 519 and 538.

LCM(519,538) = 3¹ × 173¹ × 2¹ × 269¹
LCM(519,538) = 279222