What is the Least Common Multiple of 44100 and 44114?

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 44100 and 44114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 44100 and 44114, than apply into the LCM equation.

GCF(44100,44114) = 14
LCM(44100,44114) = ( 44100 × 44114) / 14
LCM(44100,44114) = 1945427400 / 14
LCM(44100,44114) = 138959100

Least Common Multiple (LCM) of 44100 and 44114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 44100 and 44114. First we will calculate the prime factors of 44100 and 44114.

Prime Factorization of 44100

Prime Factorization of 44114

Now multiplying the highest exponent prime factors to calculate the LCM of 44100 and 44114.

LCM(44100,44114) = 2² × 3² × 5² × 7² × 23¹ × 137¹
LCM(44100,44114) = 138959100