What is the Least Common Multiple of 105 and 168?

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 105 and 168 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 168, than apply into the LCM equation.

GCF(105,168) = 21
LCM(105,168) = ( 105 × 168) / 21
LCM(105,168) = 17640 / 21
LCM(105,168) = 840

Least Common Multiple (LCM) of 105 and 168 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 168. First we will calculate the prime factors of 105 and 168.

Prime Factorization of 105

Prime Factorization of 168

Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 168.

LCM(105,168) = 3¹ × 5¹ × 7¹ × 2³
LCM(105,168) = 840