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What is the Least Common Multiple of 30138 and 30147?

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 30138 and 30147 is 302856762.

LCM(30138,30147) = 302856762

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Least Common Multiple of 30138 and 30147 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30138 and 30147, than apply into the LCM equation.

GCF(30138,30147) = 3
LCM(30138,30147) = ( 30138 × 30147) / 3
LCM(30138,30147) = 908570286 / 3
LCM(30138,30147) = 302856762

Least Common Multiple (LCM) of 30138 and 30147 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30138 and 30147. First we will calculate the prime factors of 30138 and 30147.

Prime Factorization of 30138

Prime factors of 30138 are 2, 3, 5023. Prime factorization of 30138 in exponential form is:

30138 = 21 × 31 × 50231

Prime Factorization of 30147

Prime factors of 30147 are 3, 13, 773. Prime factorization of 30147 in exponential form is:

30147 = 31 × 131 × 7731

Now multiplying the highest exponent prime factors to calculate the LCM of 30138 and 30147.

LCM(30138,30147) = 21 × 31 × 50231 × 131 × 7731
LCM(30138,30147) = 302856762