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What is the Least Common Multiple of 10569 and 10580?

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 10569 and 10580 is 111820020.

LCM(10569,10580) = 111820020

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Least Common Multiple of 10569 and 10580 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10569 and 10580, than apply into the LCM equation.

GCF(10569,10580) = 1
LCM(10569,10580) = ( 10569 × 10580) / 1
LCM(10569,10580) = 111820020 / 1
LCM(10569,10580) = 111820020

Least Common Multiple (LCM) of 10569 and 10580 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10569 and 10580. First we will calculate the prime factors of 10569 and 10580.

Prime Factorization of 10569

Prime factors of 10569 are 3, 13, 271. Prime factorization of 10569 in exponential form is:

10569 = 31 × 131 × 2711

Prime Factorization of 10580

Prime factors of 10580 are 2, 5, 23. Prime factorization of 10580 in exponential form is:

10580 = 22 × 51 × 232

Now multiplying the highest exponent prime factors to calculate the LCM of 10569 and 10580.

LCM(10569,10580) = 31 × 131 × 2711 × 22 × 51 × 232
LCM(10569,10580) = 111820020