What is the Least Common Multiple of 5138 and 5152?

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 5138 and 5152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5138 and 5152, than apply into the LCM equation.

GCF(5138,5152) = 14
LCM(5138,5152) = ( 5138 × 5152) / 14
LCM(5138,5152) = 26470976 / 14
LCM(5138,5152) = 1890784

Least Common Multiple (LCM) of 5138 and 5152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5138 and 5152. First we will calculate the prime factors of 5138 and 5152.

Prime Factorization of 5138

Prime Factorization of 5152

Now multiplying the highest exponent prime factors to calculate the LCM of 5138 and 5152.

LCM(5138,5152) = 2⁵ × 7¹ × 367¹ × 23¹
LCM(5138,5152) = 1890784