What is the Least Common Multiple of 49920 and 49938?

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 49920 and 49938 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49920 and 49938, than apply into the LCM equation.

GCF(49920,49938) = 6
LCM(49920,49938) = ( 49920 × 49938) / 6
LCM(49920,49938) = 2492904960 / 6
LCM(49920,49938) = 415484160

Least Common Multiple (LCM) of 49920 and 49938 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49920 and 49938. First we will calculate the prime factors of 49920 and 49938.

Prime Factorization of 49920

Prime Factorization of 49938

Now multiplying the highest exponent prime factors to calculate the LCM of 49920 and 49938.

LCM(49920,49938) = 2⁸ × 3¹ × 5¹ × 13¹ × 7¹ × 29¹ × 41¹
LCM(49920,49938) = 415484160