What is the Least Common Multiple of 900 and 916?

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 900 and 916 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 900 and 916, than apply into the LCM equation.

GCF(900,916) = 4
LCM(900,916) = ( 900 × 916) / 4
LCM(900,916) = 824400 / 4
LCM(900,916) = 206100

Least Common Multiple (LCM) of 900 and 916 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 900 and 916. First we will calculate the prime factors of 900 and 916.

Prime Factorization of 900

Prime Factorization of 916

Now multiplying the highest exponent prime factors to calculate the LCM of 900 and 916.

LCM(900,916) = 2² × 3² × 5² × 229¹
LCM(900,916) = 206100