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What is the Least Common Multiple of 30678 and 30698?

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 30678 and 30698 is 470876622.

LCM(30678,30698) = 470876622

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Least Common Multiple of 30678 and 30698 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30678 and 30698, than apply into the LCM equation.

GCF(30678,30698) = 2
LCM(30678,30698) = ( 30678 × 30698) / 2
LCM(30678,30698) = 941753244 / 2
LCM(30678,30698) = 470876622

Least Common Multiple (LCM) of 30678 and 30698 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30678 and 30698. First we will calculate the prime factors of 30678 and 30698.

Prime Factorization of 30678

Prime factors of 30678 are 2, 3, 5113. Prime factorization of 30678 in exponential form is:

30678 = 21 × 31 × 51131

Prime Factorization of 30698

Prime factors of 30698 are 2, 15349. Prime factorization of 30698 in exponential form is:

30698 = 21 × 153491

Now multiplying the highest exponent prime factors to calculate the LCM of 30678 and 30698.

LCM(30678,30698) = 21 × 31 × 51131 × 153491
LCM(30678,30698) = 470876622