What is the Least Common Multiple of 40 and 256?

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 40 and 256 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 256, than apply into the LCM equation.

GCF(40,256) = 8
LCM(40,256) = ( 40 × 256) / 8
LCM(40,256) = 10240 / 8
LCM(40,256) = 1280

Least Common Multiple (LCM) of 40 and 256 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 256. First we will calculate the prime factors of 40 and 256.

Prime Factorization of 40

Prime Factorization of 256

Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 256.

LCM(40,256) = 2⁸ × 5¹
LCM(40,256) = 1280