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What is the Least Common Multiple of 10509 and 10523?

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 10509 and 10523 is 110586207.

LCM(10509,10523) = 110586207

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Least Common Multiple of 10509 and 10523 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10509 and 10523, than apply into the LCM equation.

GCF(10509,10523) = 1
LCM(10509,10523) = ( 10509 × 10523) / 1
LCM(10509,10523) = 110586207 / 1
LCM(10509,10523) = 110586207

Least Common Multiple (LCM) of 10509 and 10523 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10509 and 10523. First we will calculate the prime factors of 10509 and 10523.

Prime Factorization of 10509

Prime factors of 10509 are 3, 31, 113. Prime factorization of 10509 in exponential form is:

10509 = 31 × 311 × 1131

Prime Factorization of 10523

Prime factors of 10523 are 17, 619. Prime factorization of 10523 in exponential form is:

10523 = 171 × 6191

Now multiplying the highest exponent prime factors to calculate the LCM of 10509 and 10523.

LCM(10509,10523) = 31 × 311 × 1131 × 171 × 6191
LCM(10509,10523) = 110586207