What is the Least Common Multiple of 21900 and 21912?

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 21900 and 21912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21900 and 21912, than apply into the LCM equation.

GCF(21900,21912) = 12
LCM(21900,21912) = ( 21900 × 21912) / 12
LCM(21900,21912) = 479872800 / 12
LCM(21900,21912) = 39989400

Least Common Multiple (LCM) of 21900 and 21912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21900 and 21912. First we will calculate the prime factors of 21900 and 21912.

Prime Factorization of 21900

Prime Factorization of 21912

Now multiplying the highest exponent prime factors to calculate the LCM of 21900 and 21912.

LCM(21900,21912) = 2³ × 3¹ × 5² × 73¹ × 11¹ × 83¹
LCM(21900,21912) = 39989400