What is the Least Common Multiple of 21300 and 21318?

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 21318 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 21318, than apply into the LCM equation.

GCF(21300,21318) = 6
LCM(21300,21318) = ( 21300 × 21318) / 6
LCM(21300,21318) = 454073400 / 6
LCM(21300,21318) = 75678900

Least Common Multiple (LCM) of 21300 and 21318 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21300 and 21318. First we will calculate the prime factors of 21300 and 21318.

Prime Factorization of 21300

Prime Factorization of 21318

Now multiplying the highest exponent prime factors to calculate the LCM of 21300 and 21318.

LCM(21300,21318) = 2² × 3¹ × 5² × 71¹ × 11¹ × 17¹ × 19¹
LCM(21300,21318) = 75678900