What is the Least Common Multiple of 39546 and 39552?

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 39546 and 39552 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39546 and 39552, than apply into the LCM equation.

GCF(39546,39552) = 6
LCM(39546,39552) = ( 39546 × 39552) / 6
LCM(39546,39552) = 1564123392 / 6
LCM(39546,39552) = 260687232

Least Common Multiple (LCM) of 39546 and 39552 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39546 and 39552. First we will calculate the prime factors of 39546 and 39552.

Prime Factorization of 39546

Prime Factorization of 39552

Now multiplying the highest exponent prime factors to calculate the LCM of 39546 and 39552.

LCM(39546,39552) = 2⁷ × 3² × 13³ × 103¹
LCM(39546,39552) = 260687232