What is the Least Common Multiple of 69072 and 69084?

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 69072 and 69084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69072 and 69084, than apply into the LCM equation.

GCF(69072,69084) = 12
LCM(69072,69084) = ( 69072 × 69084) / 12
LCM(69072,69084) = 4771770048 / 12
LCM(69072,69084) = 397647504

Least Common Multiple (LCM) of 69072 and 69084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69072 and 69084. First we will calculate the prime factors of 69072 and 69084.

Prime Factorization of 69072

Prime Factorization of 69084

Now multiplying the highest exponent prime factors to calculate the LCM of 69072 and 69084.

LCM(69072,69084) = 2⁴ × 3² × 1439¹ × 19¹ × 101¹
LCM(69072,69084) = 397647504