What is the Least Common Multiple of 23250 and 23264?

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 23250 and 23264 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23250 and 23264, than apply into the LCM equation.

GCF(23250,23264) = 2
LCM(23250,23264) = ( 23250 × 23264) / 2
LCM(23250,23264) = 540888000 / 2
LCM(23250,23264) = 270444000

Least Common Multiple (LCM) of 23250 and 23264 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23250 and 23264. First we will calculate the prime factors of 23250 and 23264.

Prime Factorization of 23250

Prime Factorization of 23264

Now multiplying the highest exponent prime factors to calculate the LCM of 23250 and 23264.

LCM(23250,23264) = 2⁵ × 3¹ × 5³ × 31¹ × 727¹
LCM(23250,23264) = 270444000