What is the Least Common Multiple of 49180 and 49200?

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 49180 and 49200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49180 and 49200, than apply into the LCM equation.

GCF(49180,49200) = 20
LCM(49180,49200) = ( 49180 × 49200) / 20
LCM(49180,49200) = 2419656000 / 20
LCM(49180,49200) = 120982800

Least Common Multiple (LCM) of 49180 and 49200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49180 and 49200. First we will calculate the prime factors of 49180 and 49200.

Prime Factorization of 49180

Prime Factorization of 49200

Now multiplying the highest exponent prime factors to calculate the LCM of 49180 and 49200.

LCM(49180,49200) = 2⁴ × 5² × 2459¹ × 3¹ × 41¹
LCM(49180,49200) = 120982800