What is the Least Common Multiple of 36900 and 36912?

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 36900 and 36912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36900 and 36912, than apply into the LCM equation.

GCF(36900,36912) = 12
LCM(36900,36912) = ( 36900 × 36912) / 12
LCM(36900,36912) = 1362052800 / 12
LCM(36900,36912) = 113504400

Least Common Multiple (LCM) of 36900 and 36912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36900 and 36912. First we will calculate the prime factors of 36900 and 36912.

Prime Factorization of 36900

Prime Factorization of 36912

Now multiplying the highest exponent prime factors to calculate the LCM of 36900 and 36912.

LCM(36900,36912) = 2⁴ × 3² × 5² × 41¹ × 769¹
LCM(36900,36912) = 113504400