What is the Least Common Multiple of 21420 and 21432?

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 21420 and 21432 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21420 and 21432, than apply into the LCM equation.

GCF(21420,21432) = 12
LCM(21420,21432) = ( 21420 × 21432) / 12
LCM(21420,21432) = 459073440 / 12
LCM(21420,21432) = 38256120

Least Common Multiple (LCM) of 21420 and 21432 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21420 and 21432. First we will calculate the prime factors of 21420 and 21432.

Prime Factorization of 21420

Prime Factorization of 21432

Now multiplying the highest exponent prime factors to calculate the LCM of 21420 and 21432.

LCM(21420,21432) = 2³ × 3² × 5¹ × 7¹ × 17¹ × 19¹ × 47¹
LCM(21420,21432) = 38256120