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What is the Least Common Multiple of 30552 and 30560?

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 30552 and 30560 is 116708640.

LCM(30552,30560) = 116708640

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Least Common Multiple of 30552 and 30560 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30552 and 30560, than apply into the LCM equation.

GCF(30552,30560) = 8
LCM(30552,30560) = ( 30552 × 30560) / 8
LCM(30552,30560) = 933669120 / 8
LCM(30552,30560) = 116708640

Least Common Multiple (LCM) of 30552 and 30560 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30552 and 30560. First we will calculate the prime factors of 30552 and 30560.

Prime Factorization of 30552

Prime factors of 30552 are 2, 3, 19, 67. Prime factorization of 30552 in exponential form is:

30552 = 23 × 31 × 191 × 671

Prime Factorization of 30560

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

30560 = 25 × 51 × 1911

Now multiplying the highest exponent prime factors to calculate the LCM of 30552 and 30560.

LCM(30552,30560) = 25 × 31 × 191 × 671 × 51 × 1911
LCM(30552,30560) = 116708640