What is the Least Common Multiple of 30675 and 30684?

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 30675 and 30684 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30675 and 30684, than apply into the LCM equation.

GCF(30675,30684) = 3
LCM(30675,30684) = ( 30675 × 30684) / 3
LCM(30675,30684) = 941231700 / 3
LCM(30675,30684) = 313743900

Least Common Multiple (LCM) of 30675 and 30684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30675 and 30684. First we will calculate the prime factors of 30675 and 30684.

Prime Factorization of 30675

Prime Factorization of 30684

Now multiplying the highest exponent prime factors to calculate the LCM of 30675 and 30684.

LCM(30675,30684) = 3¹ × 5² × 409¹ × 2² × 2557¹
LCM(30675,30684) = 313743900