What is the Least Common Multiple of 47992 and 48000?

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 47992 and 48000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 47992 and 48000, than apply into the LCM equation.

GCF(47992,48000) = 8
LCM(47992,48000) = ( 47992 × 48000) / 8
LCM(47992,48000) = 2303616000 / 8
LCM(47992,48000) = 287952000

Least Common Multiple (LCM) of 47992 and 48000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 47992 and 48000. First we will calculate the prime factors of 47992 and 48000.

Prime Factorization of 47992

Prime Factorization of 48000

Now multiplying the highest exponent prime factors to calculate the LCM of 47992 and 48000.

LCM(47992,48000) = 2⁷ × 7¹ × 857¹ × 3¹ × 5³
LCM(47992,48000) = 287952000