What is the Least Common Multiple of 21285 and 21300?

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 21285 and 21300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21285 and 21300, than apply into the LCM equation.

GCF(21285,21300) = 15
LCM(21285,21300) = ( 21285 × 21300) / 15
LCM(21285,21300) = 453370500 / 15
LCM(21285,21300) = 30224700

Least Common Multiple (LCM) of 21285 and 21300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21285 and 21300. First we will calculate the prime factors of 21285 and 21300.

Prime Factorization of 21285

Prime Factorization of 21300

Now multiplying the highest exponent prime factors to calculate the LCM of 21285 and 21300.

LCM(21285,21300) = 3² × 5² × 11¹ × 43¹ × 2² × 71¹
LCM(21285,21300) = 30224700