What is the Least Common Multiple of 47712 and 47728?

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 47712 and 47728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 47712 and 47728, than apply into the LCM equation.

GCF(47712,47728) = 16
LCM(47712,47728) = ( 47712 × 47728) / 16
LCM(47712,47728) = 2277198336 / 16
LCM(47712,47728) = 142324896

Least Common Multiple (LCM) of 47712 and 47728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 47712 and 47728. First we will calculate the prime factors of 47712 and 47728.

Prime Factorization of 47712

Prime Factorization of 47728

Now multiplying the highest exponent prime factors to calculate the LCM of 47712 and 47728.

LCM(47712,47728) = 2⁵ × 3¹ × 7¹ × 71¹ × 19¹ × 157¹
LCM(47712,47728) = 142324896