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What is the Least Common Multiple of 30986 and 31004?

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 30986 and 31004 is 480344972.

LCM(30986,31004) = 480344972

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Least Common Multiple of 30986 and 31004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30986 and 31004, than apply into the LCM equation.

GCF(30986,31004) = 2
LCM(30986,31004) = ( 30986 × 31004) / 2
LCM(30986,31004) = 960689944 / 2
LCM(30986,31004) = 480344972

Least Common Multiple (LCM) of 30986 and 31004 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30986 and 31004. First we will calculate the prime factors of 30986 and 31004.

Prime Factorization of 30986

Prime factors of 30986 are 2, 15493. Prime factorization of 30986 in exponential form is:

30986 = 21 × 154931

Prime Factorization of 31004

Prime factors of 31004 are 2, 23, 337. Prime factorization of 31004 in exponential form is:

31004 = 22 × 231 × 3371

Now multiplying the highest exponent prime factors to calculate the LCM of 30986 and 31004.

LCM(30986,31004) = 22 × 154931 × 231 × 3371
LCM(30986,31004) = 480344972