What is the Least Common Multiple of 168 and 172?

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 172 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 172, than apply into the LCM equation.

GCF(168,172) = 4
LCM(168,172) = ( 168 × 172) / 4
LCM(168,172) = 28896 / 4
LCM(168,172) = 7224

Least Common Multiple (LCM) of 168 and 172 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 168 and 172. First we will calculate the prime factors of 168 and 172.

Prime Factorization of 168

Prime Factorization of 172

Now multiplying the highest exponent prime factors to calculate the LCM of 168 and 172.

LCM(168,172) = 2³ × 3¹ × 7¹ × 43¹
LCM(168,172) = 7224