What is the Least Common Multiple of 238 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 238 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 238 and 256, than apply into the LCM equation.

GCF(238,256) = 2
LCM(238,256) = ( 238 × 256) / 2
LCM(238,256) = 60928 / 2
LCM(238,256) = 30464

Least Common Multiple (LCM) of 238 and 256 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 238 and 256. First we will calculate the prime factors of 238 and 256.

Prime Factorization of 238

Prime Factorization of 256

Now multiplying the highest exponent prime factors to calculate the LCM of 238 and 256.

LCM(238,256) = 2⁸ × 7¹ × 17¹
LCM(238,256) = 30464