What is the Least Common Multiple of 420 and 432?

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 420 and 432 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 432, than apply into the LCM equation.

GCF(420,432) = 12
LCM(420,432) = ( 420 × 432) / 12
LCM(420,432) = 181440 / 12
LCM(420,432) = 15120

Least Common Multiple (LCM) of 420 and 432 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 432. First we will calculate the prime factors of 420 and 432.

Prime Factorization of 420

Prime Factorization of 432

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 432.

LCM(420,432) = 2⁴ × 3³ × 5¹ × 7¹
LCM(420,432) = 15120