What is the Least Common Multiple of 72180 and 72184?

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 72180 and 72184 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72180 and 72184, than apply into the LCM equation.

GCF(72180,72184) = 4
LCM(72180,72184) = ( 72180 × 72184) / 4
LCM(72180,72184) = 5210241120 / 4
LCM(72180,72184) = 1302560280

Least Common Multiple (LCM) of 72180 and 72184 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72180 and 72184. First we will calculate the prime factors of 72180 and 72184.

Prime Factorization of 72180

Prime Factorization of 72184

Now multiplying the highest exponent prime factors to calculate the LCM of 72180 and 72184.

LCM(72180,72184) = 2³ × 3² × 5¹ × 401¹ × 7¹ × 1289¹
LCM(72180,72184) = 1302560280