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What is the Least Common Multiple of 30560 and 30566?

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 30560 and 30566 is 467048480.

LCM(30560,30566) = 467048480

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Least Common Multiple of 30560 and 30566 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30560 and 30566, than apply into the LCM equation.

GCF(30560,30566) = 2
LCM(30560,30566) = ( 30560 × 30566) / 2
LCM(30560,30566) = 934096960 / 2
LCM(30560,30566) = 467048480

Least Common Multiple (LCM) of 30560 and 30566 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30560 and 30566. First we will calculate the prime factors of 30560 and 30566.

Prime Factorization of 30560

Prime factors of 30560 are 2, 5, 191. Prime factorization of 30560 in exponential form is:

30560 = 25 × 51 × 1911

Prime Factorization of 30566

Prime factors of 30566 are 2, 17, 29, 31. Prime factorization of 30566 in exponential form is:

30566 = 21 × 171 × 291 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 30560 and 30566.

LCM(30560,30566) = 25 × 51 × 1911 × 171 × 291 × 311
LCM(30560,30566) = 467048480