What is the Least Common Multiple of 224 and 238?

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 224 and 238 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 224 and 238, than apply into the LCM equation.

GCF(224,238) = 14
LCM(224,238) = ( 224 × 238) / 14
LCM(224,238) = 53312 / 14
LCM(224,238) = 3808

Least Common Multiple (LCM) of 224 and 238 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 224 and 238. First we will calculate the prime factors of 224 and 238.

Prime Factorization of 224

Prime Factorization of 238

Now multiplying the highest exponent prime factors to calculate the LCM of 224 and 238.

LCM(224,238) = 2⁵ × 7¹ × 17¹
LCM(224,238) = 3808