What is the Least Common Multiple of 82260 and 82272?

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 82260 and 82272 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82260 and 82272, than apply into the LCM equation.

GCF(82260,82272) = 12
LCM(82260,82272) = ( 82260 × 82272) / 12
LCM(82260,82272) = 6767694720 / 12
LCM(82260,82272) = 563974560

Least Common Multiple (LCM) of 82260 and 82272 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82260 and 82272. First we will calculate the prime factors of 82260 and 82272.

Prime Factorization of 82260

Prime Factorization of 82272

Now multiplying the highest exponent prime factors to calculate the LCM of 82260 and 82272.

LCM(82260,82272) = 2⁵ × 3² × 5¹ × 457¹ × 857¹
LCM(82260,82272) = 563974560