What is the Least Common Multiple of 18 and 174?

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 18 and 174 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18 and 174, than apply into the LCM equation.

GCF(18,174) = 6
LCM(18,174) = ( 18 × 174) / 6
LCM(18,174) = 3132 / 6
LCM(18,174) = 522

Least Common Multiple (LCM) of 18 and 174 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18 and 174. First we will calculate the prime factors of 18 and 174.

Prime Factorization of 18

Prime Factorization of 174

Now multiplying the highest exponent prime factors to calculate the LCM of 18 and 174.

LCM(18,174) = 2¹ × 3² × 29¹
LCM(18,174) = 522