What is the Least Common Multiple of 23100 and 23114?

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 23100 and 23114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23100 and 23114, than apply into the LCM equation.

GCF(23100,23114) = 14
LCM(23100,23114) = ( 23100 × 23114) / 14
LCM(23100,23114) = 533933400 / 14
LCM(23100,23114) = 38138100

Least Common Multiple (LCM) of 23100 and 23114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23100 and 23114. First we will calculate the prime factors of 23100 and 23114.

Prime Factorization of 23100

Prime Factorization of 23114

Now multiplying the highest exponent prime factors to calculate the LCM of 23100 and 23114.

LCM(23100,23114) = 2² × 3¹ × 5² × 7¹ × 11¹ × 13¹ × 127¹
LCM(23100,23114) = 38138100