What is the Least Common Multiple of 314 and 322?

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 314 and 322 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 314 and 322, than apply into the LCM equation.

GCF(314,322) = 2
LCM(314,322) = ( 314 × 322) / 2
LCM(314,322) = 101108 / 2
LCM(314,322) = 50554

Least Common Multiple (LCM) of 314 and 322 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 322. First we will calculate the prime factors of 314 and 322.

Prime Factorization of 314

Prime Factorization of 322

Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 322.

LCM(314,322) = 2¹ × 157¹ × 7¹ × 23¹
LCM(314,322) = 50554