What is the Least Common Multiple of 49008 and 49023?

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 49008 and 49023 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49008 and 49023, than apply into the LCM equation.

GCF(49008,49023) = 3
LCM(49008,49023) = ( 49008 × 49023) / 3
LCM(49008,49023) = 2402519184 / 3
LCM(49008,49023) = 800839728

Least Common Multiple (LCM) of 49008 and 49023 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49008 and 49023. First we will calculate the prime factors of 49008 and 49023.

Prime Factorization of 49008

Prime Factorization of 49023

Now multiplying the highest exponent prime factors to calculate the LCM of 49008 and 49023.

LCM(49008,49023) = 2⁴ × 3² × 1021¹ × 13¹ × 419¹
LCM(49008,49023) = 800839728