What is the Least Common Multiple of 30576 and 30582?

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 30576 and 30582 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30576 and 30582, than apply into the LCM equation.

GCF(30576,30582) = 6
LCM(30576,30582) = ( 30576 × 30582) / 6
LCM(30576,30582) = 935075232 / 6
LCM(30576,30582) = 155845872

Least Common Multiple (LCM) of 30576 and 30582 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30576 and 30582. First we will calculate the prime factors of 30576 and 30582.

Prime Factorization of 30576

Prime Factorization of 30582

Now multiplying the highest exponent prime factors to calculate the LCM of 30576 and 30582.

LCM(30576,30582) = 2⁴ × 3² × 7² × 13¹ × 1699¹
LCM(30576,30582) = 155845872