What is the Least Common Multiple of 72144 and 72162?

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 72144 and 72162 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72144 and 72162, than apply into the LCM equation.

GCF(72144,72162) = 18
LCM(72144,72162) = ( 72144 × 72162) / 18
LCM(72144,72162) = 5206055328 / 18
LCM(72144,72162) = 289225296

Least Common Multiple (LCM) of 72144 and 72162 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72144 and 72162. First we will calculate the prime factors of 72144 and 72162.

Prime Factorization of 72144

Prime Factorization of 72162

Now multiplying the highest exponent prime factors to calculate the LCM of 72144 and 72162.

LCM(72144,72162) = 2⁴ × 3³ × 167¹ × 19¹ × 211¹
LCM(72144,72162) = 289225296