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What is the Least Common Multiple of 10514 and 10518?

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 10514 and 10518 is 55293126.

LCM(10514,10518) = 55293126

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Least Common Multiple of 10514 and 10518 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10514 and 10518, than apply into the LCM equation.

GCF(10514,10518) = 2
LCM(10514,10518) = ( 10514 × 10518) / 2
LCM(10514,10518) = 110586252 / 2
LCM(10514,10518) = 55293126

Least Common Multiple (LCM) of 10514 and 10518 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10514 and 10518. First we will calculate the prime factors of 10514 and 10518.

Prime Factorization of 10514

Prime factors of 10514 are 2, 7, 751. Prime factorization of 10514 in exponential form is:

10514 = 21 × 71 × 7511

Prime Factorization of 10518

Prime factors of 10518 are 2, 3, 1753. Prime factorization of 10518 in exponential form is:

10518 = 21 × 31 × 17531

Now multiplying the highest exponent prime factors to calculate the LCM of 10514 and 10518.

LCM(10514,10518) = 21 × 71 × 7511 × 31 × 17531
LCM(10514,10518) = 55293126