What is the Least Common Multiple of 65100 and 65114?

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 65100 and 65114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65100 and 65114, than apply into the LCM equation.

GCF(65100,65114) = 14
LCM(65100,65114) = ( 65100 × 65114) / 14
LCM(65100,65114) = 4238921400 / 14
LCM(65100,65114) = 302780100

Least Common Multiple (LCM) of 65100 and 65114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65100 and 65114. First we will calculate the prime factors of 65100 and 65114.

Prime Factorization of 65100

Prime Factorization of 65114

Now multiplying the highest exponent prime factors to calculate the LCM of 65100 and 65114.

LCM(65100,65114) = 2² × 3¹ × 5² × 7¹ × 31¹ × 4651¹
LCM(65100,65114) = 302780100