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What is the Least Common Multiple of 30117 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 30117 and 30132 is 302495148.

LCM(30117,30132) = 302495148

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Least Common Multiple of 30117 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 30117 and 30132, than apply into the LCM equation.

GCF(30117,30132) = 3
LCM(30117,30132) = ( 30117 × 30132) / 3
LCM(30117,30132) = 907485444 / 3
LCM(30117,30132) = 302495148

Least Common Multiple (LCM) of 30117 and 30132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30117 and 30132. First we will calculate the prime factors of 30117 and 30132.

Prime Factorization of 30117

Prime factors of 30117 are 3, 10039. Prime factorization of 30117 in exponential form is:

30117 = 31 × 100391

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 30117 and 30132.

LCM(30117,30132) = 35 × 100391 × 22 × 311
LCM(30117,30132) = 302495148