What is the Least Common Multiple of 52100 and 52114?

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 52100 and 52114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 52100 and 52114, than apply into the LCM equation.

GCF(52100,52114) = 2
LCM(52100,52114) = ( 52100 × 52114) / 2
LCM(52100,52114) = 2715139400 / 2
LCM(52100,52114) = 1357569700

Least Common Multiple (LCM) of 52100 and 52114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 52100 and 52114. First we will calculate the prime factors of 52100 and 52114.

Prime Factorization of 52100

Prime Factorization of 52114

Now multiplying the highest exponent prime factors to calculate the LCM of 52100 and 52114.

LCM(52100,52114) = 2² × 5² × 521¹ × 71¹ × 367¹
LCM(52100,52114) = 1357569700