What is the Least Common Multiple of 72900 and 72912?

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 72900 and 72912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72900 and 72912, than apply into the LCM equation.

GCF(72900,72912) = 12
LCM(72900,72912) = ( 72900 × 72912) / 12
LCM(72900,72912) = 5315284800 / 12
LCM(72900,72912) = 442940400

Least Common Multiple (LCM) of 72900 and 72912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72900 and 72912. First we will calculate the prime factors of 72900 and 72912.

Prime Factorization of 72900

Prime Factorization of 72912

Now multiplying the highest exponent prime factors to calculate the LCM of 72900 and 72912.

LCM(72900,72912) = 2⁴ × 3⁶ × 5² × 7² × 31¹
LCM(72900,72912) = 442940400