What is the Least Common Multiple of 78546 and 78564?

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 78546 and 78564 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78546 and 78564, than apply into the LCM equation.

GCF(78546,78564) = 6
LCM(78546,78564) = ( 78546 × 78564) / 6
LCM(78546,78564) = 6170887944 / 6
LCM(78546,78564) = 1028481324

Least Common Multiple (LCM) of 78546 and 78564 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78546 and 78564. First we will calculate the prime factors of 78546 and 78564.

Prime Factorization of 78546

Prime Factorization of 78564

Now multiplying the highest exponent prime factors to calculate the LCM of 78546 and 78564.

LCM(78546,78564) = 2² × 3¹ × 13¹ × 19¹ × 53¹ × 6547¹
LCM(78546,78564) = 1028481324