What is the Least Common Multiple of 305 and 314?

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 305 and 314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 305 and 314, than apply into the LCM equation.

GCF(305,314) = 1
LCM(305,314) = ( 305 × 314) / 1
LCM(305,314) = 95770 / 1
LCM(305,314) = 95770

Least Common Multiple (LCM) of 305 and 314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 305 and 314. First we will calculate the prime factors of 305 and 314.

Prime Factorization of 305

Prime Factorization of 314

Now multiplying the highest exponent prime factors to calculate the LCM of 305 and 314.

LCM(305,314) = 5¹ × 61¹ × 2¹ × 157¹
LCM(305,314) = 95770