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What is the Least Common Multiple of 10569 and 10575?

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 10575 is 37255725.

LCM(10569,10575) = 37255725

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Least Common Multiple of 10569 and 10575 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 10575, than apply into the LCM equation.

GCF(10569,10575) = 3
LCM(10569,10575) = ( 10569 × 10575) / 3
LCM(10569,10575) = 111767175 / 3
LCM(10569,10575) = 37255725

Least Common Multiple (LCM) of 10569 and 10575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10569 and 10575. First we will calculate the prime factors of 10569 and 10575.

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 10575

Prime factors of 10575 are 3, 5, 47. Prime factorization of 10575 in exponential form is:

10575 = 32 × 52 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 10569 and 10575.

LCM(10569,10575) = 32 × 131 × 2711 × 52 × 471
LCM(10569,10575) = 37255725