What is the Least Common Multiple of 10128 and 10138?

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 10128 and 10138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10128 and 10138, than apply into the LCM equation.

GCF(10128,10138) = 2
LCM(10128,10138) = ( 10128 × 10138) / 2
LCM(10128,10138) = 102677664 / 2
LCM(10128,10138) = 51338832

Least Common Multiple (LCM) of 10128 and 10138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10128 and 10138. First we will calculate the prime factors of 10128 and 10138.

Prime Factorization of 10128

Prime Factorization of 10138

Now multiplying the highest exponent prime factors to calculate the LCM of 10128 and 10138.

LCM(10128,10138) = 2⁴ × 3¹ × 211¹ × 37¹ × 137¹
LCM(10128,10138) = 51338832