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What is the Least Common Multiple of 72144 and 72148?

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 (LCM) of 72144 and 72148 is 1301261328.

LCM(72144,72148) = 1301261328

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Least Common Multiple of 72144 and 72148 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 72148, than apply into the LCM equation.

GCF(72144,72148) = 4
LCM(72144,72148) = ( 72144 × 72148) / 4
LCM(72144,72148) = 5205045312 / 4
LCM(72144,72148) = 1301261328

Least Common Multiple (LCM) of 72144 and 72148 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72144 and 72148. First we will calculate the prime factors of 72144 and 72148.

Prime Factorization of 72144

Prime factors of 72144 are 2, 3, 167. Prime factorization of 72144 in exponential form is:

72144 = 24 × 33 × 1671

Prime Factorization of 72148

Prime factors of 72148 are 2, 17, 1061. Prime factorization of 72148 in exponential form is:

72148 = 22 × 171 × 10611

Now multiplying the highest exponent prime factors to calculate the LCM of 72144 and 72148.

LCM(72144,72148) = 24 × 33 × 1671 × 171 × 10611
LCM(72144,72148) = 1301261328