What is the Least Common Multiple of 51300 and 51319?

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 51300 and 51319 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51300 and 51319, than apply into the LCM equation.

GCF(51300,51319) = 19
LCM(51300,51319) = ( 51300 × 51319) / 19
LCM(51300,51319) = 2632664700 / 19
LCM(51300,51319) = 138561300

Least Common Multiple (LCM) of 51300 and 51319 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51300 and 51319. First we will calculate the prime factors of 51300 and 51319.

Prime Factorization of 51300

Prime Factorization of 51319

Now multiplying the highest exponent prime factors to calculate the LCM of 51300 and 51319.

LCM(51300,51319) = 2² × 3³ × 5² × 19¹ × 37¹ × 73¹
LCM(51300,51319) = 138561300