What is the Least Common Multiple of 21300 and 21312?

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 21300 and 21312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21300 and 21312, than apply into the LCM equation.

GCF(21300,21312) = 12
LCM(21300,21312) = ( 21300 × 21312) / 12
LCM(21300,21312) = 453945600 / 12
LCM(21300,21312) = 37828800

Least Common Multiple (LCM) of 21300 and 21312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21300 and 21312. First we will calculate the prime factors of 21300 and 21312.

Prime Factorization of 21300

Prime Factorization of 21312

Now multiplying the highest exponent prime factors to calculate the LCM of 21300 and 21312.

LCM(21300,21312) = 2⁶ × 3² × 5² × 71¹ × 37¹
LCM(21300,21312) = 37828800