What is the Least Common Multiple of 174 and 189?

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 174 and 189 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 174 and 189, than apply into the LCM equation.

GCF(174,189) = 3
LCM(174,189) = ( 174 × 189) / 3
LCM(174,189) = 32886 / 3
LCM(174,189) = 10962

Least Common Multiple (LCM) of 174 and 189 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 174 and 189. First we will calculate the prime factors of 174 and 189.

Prime Factorization of 174

Prime Factorization of 189

Now multiplying the highest exponent prime factors to calculate the LCM of 174 and 189.

LCM(174,189) = 2¹ × 3³ × 29¹ × 7¹
LCM(174,189) = 10962