What is the Least Common Multiple of 34125 and 34138?

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 34125 and 34138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34125 and 34138, than apply into the LCM equation.

GCF(34125,34138) = 13
LCM(34125,34138) = ( 34125 × 34138) / 13
LCM(34125,34138) = 1164959250 / 13
LCM(34125,34138) = 89612250

Least Common Multiple (LCM) of 34125 and 34138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34125 and 34138. First we will calculate the prime factors of 34125 and 34138.

Prime Factorization of 34125

Prime Factorization of 34138

Now multiplying the highest exponent prime factors to calculate the LCM of 34125 and 34138.

LCM(34125,34138) = 3¹ × 5³ × 7¹ × 13² × 2¹ × 101¹
LCM(34125,34138) = 89612250