What is the Least Common Multiple of 5096 and 5114?

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 5096 and 5114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5096 and 5114, than apply into the LCM equation.

GCF(5096,5114) = 2
LCM(5096,5114) = ( 5096 × 5114) / 2
LCM(5096,5114) = 26060944 / 2
LCM(5096,5114) = 13030472

Least Common Multiple (LCM) of 5096 and 5114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5096 and 5114. First we will calculate the prime factors of 5096 and 5114.

Prime Factorization of 5096

Prime Factorization of 5114

Now multiplying the highest exponent prime factors to calculate the LCM of 5096 and 5114.

LCM(5096,5114) = 2³ × 7² × 13¹ × 2557¹
LCM(5096,5114) = 13030472