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What is the Least Common Multiple of 30680 and 30686?

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 30680 and 30686 is 470723240.

LCM(30680,30686) = 470723240

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Least Common Multiple of 30680 and 30686 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30680 and 30686, than apply into the LCM equation.

GCF(30680,30686) = 2
LCM(30680,30686) = ( 30680 × 30686) / 2
LCM(30680,30686) = 941446480 / 2
LCM(30680,30686) = 470723240

Least Common Multiple (LCM) of 30680 and 30686 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30680 and 30686. First we will calculate the prime factors of 30680 and 30686.

Prime Factorization of 30680

Prime factors of 30680 are 2, 5, 13, 59. Prime factorization of 30680 in exponential form is:

30680 = 23 × 51 × 131 × 591

Prime Factorization of 30686

Prime factors of 30686 are 2, 67, 229. Prime factorization of 30686 in exponential form is:

30686 = 21 × 671 × 2291

Now multiplying the highest exponent prime factors to calculate the LCM of 30680 and 30686.

LCM(30680,30686) = 23 × 51 × 131 × 591 × 671 × 2291
LCM(30680,30686) = 470723240