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What is the Least Common Multiple of 30128 and 30132?

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 30132 is 226954224.

LCM(30128,30132) = 226954224

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Least Common Multiple of 30128 and 30132 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 30132, than apply into the LCM equation.

GCF(30128,30132) = 4
LCM(30128,30132) = ( 30128 × 30132) / 4
LCM(30128,30132) = 907816896 / 4
LCM(30128,30132) = 226954224

Least Common Multiple (LCM) of 30128 and 30132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30128 and 30132. First we will calculate the prime factors of 30128 and 30132.

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 30132

Prime factors of 30132 are 2, 3, 31. Prime factorization of 30132 in exponential form is:

30132 = 22 × 35 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 30128 and 30132.

LCM(30128,30132) = 24 × 71 × 2691 × 35 × 311
LCM(30128,30132) = 226954224