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What is the Least Common Multiple of 30128 and 30144?

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 30128 and 30144 is 56761152.

LCM(30128,30144) = 56761152

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Least Common Multiple of 30128 and 30144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30128 and 30144, than apply into the LCM equation.

GCF(30128,30144) = 16
LCM(30128,30144) = ( 30128 × 30144) / 16
LCM(30128,30144) = 908178432 / 16
LCM(30128,30144) = 56761152

Least Common Multiple (LCM) of 30128 and 30144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30128 and 30144. First we will calculate the prime factors of 30128 and 30144.

Prime Factorization of 30128

Prime factors of 30128 are 2, 7, 269. Prime factorization of 30128 in exponential form is:

30128 = 24 × 71 × 2691

Prime Factorization of 30144

Prime factors of 30144 are 2, 3, 157. Prime factorization of 30144 in exponential form is:

30144 = 26 × 31 × 1571

Now multiplying the highest exponent prime factors to calculate the LCM of 30128 and 30144.

LCM(30128,30144) = 26 × 71 × 2691 × 31 × 1571
LCM(30128,30144) = 56761152