What is the Least Common Multiple of 12750 and 12768?

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 12750 and 12768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12750 and 12768, than apply into the LCM equation.

GCF(12750,12768) = 6
LCM(12750,12768) = ( 12750 × 12768) / 6
LCM(12750,12768) = 162792000 / 6
LCM(12750,12768) = 27132000

Least Common Multiple (LCM) of 12750 and 12768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12750 and 12768. First we will calculate the prime factors of 12750 and 12768.

Prime Factorization of 12750

Prime Factorization of 12768

Now multiplying the highest exponent prime factors to calculate the LCM of 12750 and 12768.

LCM(12750,12768) = 2⁵ × 3¹ × 5³ × 17¹ × 7¹ × 19¹
LCM(12750,12768) = 27132000