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What is the Least Common Multiple of 30456 and 30464?

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 30456 and 30464 is 115976448.

LCM(30456,30464) = 115976448

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Least Common Multiple of 30456 and 30464 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30456 and 30464, than apply into the LCM equation.

GCF(30456,30464) = 8
LCM(30456,30464) = ( 30456 × 30464) / 8
LCM(30456,30464) = 927811584 / 8
LCM(30456,30464) = 115976448

Least Common Multiple (LCM) of 30456 and 30464 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30456 and 30464. First we will calculate the prime factors of 30456 and 30464.

Prime Factorization of 30456

Prime factors of 30456 are 2, 3, 47. Prime factorization of 30456 in exponential form is:

30456 = 23 × 34 × 471

Prime Factorization of 30464

Prime factors of 30464 are 2, 7, 17. Prime factorization of 30464 in exponential form is:

30464 = 28 × 71 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 30456 and 30464.

LCM(30456,30464) = 28 × 34 × 471 × 71 × 171
LCM(30456,30464) = 115976448