What is the Least Common Multiple of 891 and 900?

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 891 and 900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 891 and 900, than apply into the LCM equation.

GCF(891,900) = 9
LCM(891,900) = ( 891 × 900) / 9
LCM(891,900) = 801900 / 9
LCM(891,900) = 89100

Least Common Multiple (LCM) of 891 and 900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 891 and 900. First we will calculate the prime factors of 891 and 900.

Prime Factorization of 891

Prime Factorization of 900

Now multiplying the highest exponent prime factors to calculate the LCM of 891 and 900.

LCM(891,900) = 3⁴ × 11¹ × 2² × 5²
LCM(891,900) = 89100