What is the Least Common Multiple of 168 and 186?

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 168 and 186 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 168 and 186, than apply into the LCM equation.

GCF(168,186) = 6
LCM(168,186) = ( 168 × 186) / 6
LCM(168,186) = 31248 / 6
LCM(168,186) = 5208

Least Common Multiple (LCM) of 168 and 186 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 168 and 186. First we will calculate the prime factors of 168 and 186.

Prime Factorization of 168

Prime Factorization of 186

Now multiplying the highest exponent prime factors to calculate the LCM of 168 and 186.

LCM(168,186) = 2³ × 3¹ × 7¹ × 31¹
LCM(168,186) = 5208