What is the Least Common Multiple of 39675 and 39684?

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 39675 and 39684 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39675 and 39684, than apply into the LCM equation.

GCF(39675,39684) = 3
LCM(39675,39684) = ( 39675 × 39684) / 3
LCM(39675,39684) = 1574462700 / 3
LCM(39675,39684) = 524820900

Least Common Multiple (LCM) of 39675 and 39684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39675 and 39684. First we will calculate the prime factors of 39675 and 39684.

Prime Factorization of 39675

Prime Factorization of 39684

Now multiplying the highest exponent prime factors to calculate the LCM of 39675 and 39684.

LCM(39675,39684) = 3¹ × 5² × 23² × 2² × 3307¹
LCM(39675,39684) = 524820900