What is the Least Common Multiple of 32256 and 32270?

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 32256 and 32270 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32256 and 32270, than apply into the LCM equation.

GCF(32256,32270) = 14
LCM(32256,32270) = ( 32256 × 32270) / 14
LCM(32256,32270) = 1040901120 / 14
LCM(32256,32270) = 74350080

Least Common Multiple (LCM) of 32256 and 32270 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32256 and 32270. First we will calculate the prime factors of 32256 and 32270.

Prime Factorization of 32256

Prime Factorization of 32270

Now multiplying the highest exponent prime factors to calculate the LCM of 32256 and 32270.

LCM(32256,32270) = 2⁹ × 3² × 7¹ × 5¹ × 461¹
LCM(32256,32270) = 74350080