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What is the Least Common Multiple of 10503 and 10512?

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 10503 and 10512 is 12267504.

LCM(10503,10512) = 12267504

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Least Common Multiple of 10503 and 10512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10503 and 10512, than apply into the LCM equation.

GCF(10503,10512) = 9
LCM(10503,10512) = ( 10503 × 10512) / 9
LCM(10503,10512) = 110407536 / 9
LCM(10503,10512) = 12267504

Least Common Multiple (LCM) of 10503 and 10512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10503 and 10512. First we will calculate the prime factors of 10503 and 10512.

Prime Factorization of 10503

Prime factors of 10503 are 3, 389. Prime factorization of 10503 in exponential form is:

10503 = 33 × 3891

Prime Factorization of 10512

Prime factors of 10512 are 2, 3, 73. Prime factorization of 10512 in exponential form is:

10512 = 24 × 32 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 10503 and 10512.

LCM(10503,10512) = 33 × 3891 × 24 × 731
LCM(10503,10512) = 12267504