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What is the Least Common Multiple of 30399 and 30414?

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 30399 and 30414 is 308185062.

LCM(30399,30414) = 308185062

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Least Common Multiple of 30399 and 30414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30399 and 30414, than apply into the LCM equation.

GCF(30399,30414) = 3
LCM(30399,30414) = ( 30399 × 30414) / 3
LCM(30399,30414) = 924555186 / 3
LCM(30399,30414) = 308185062

Least Common Multiple (LCM) of 30399 and 30414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30399 and 30414. First we will calculate the prime factors of 30399 and 30414.

Prime Factorization of 30399

Prime factors of 30399 are 3, 10133. Prime factorization of 30399 in exponential form is:

30399 = 31 × 101331

Prime Factorization of 30414

Prime factors of 30414 are 2, 3, 37, 137. Prime factorization of 30414 in exponential form is:

30414 = 21 × 31 × 371 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 30399 and 30414.

LCM(30399,30414) = 31 × 101331 × 21 × 371 × 1371
LCM(30399,30414) = 308185062