What is the Least Common Multiple of 546 and 564?

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 546 and 564 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 546 and 564, than apply into the LCM equation.

GCF(546,564) = 6
LCM(546,564) = ( 546 × 564) / 6
LCM(546,564) = 307944 / 6
LCM(546,564) = 51324

Least Common Multiple (LCM) of 546 and 564 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 546 and 564. First we will calculate the prime factors of 546 and 564.

Prime Factorization of 546

Prime Factorization of 564

Now multiplying the highest exponent prime factors to calculate the LCM of 546 and 564.

LCM(546,564) = 2² × 3¹ × 7¹ × 13¹ × 47¹
LCM(546,564) = 51324