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What is the Least Common Multiple of 17736 and 17751?

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 17736 and 17751 is 104943912.

LCM(17736,17751) = 104943912

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Least Common Multiple of 17736 and 17751 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17736 and 17751, than apply into the LCM equation.

GCF(17736,17751) = 3
LCM(17736,17751) = ( 17736 × 17751) / 3
LCM(17736,17751) = 314831736 / 3
LCM(17736,17751) = 104943912

Least Common Multiple (LCM) of 17736 and 17751 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17736 and 17751. First we will calculate the prime factors of 17736 and 17751.

Prime Factorization of 17736

Prime factors of 17736 are 2, 3, 739. Prime factorization of 17736 in exponential form is:

17736 = 23 × 31 × 7391

Prime Factorization of 17751

Prime factors of 17751 are 3, 61, 97. Prime factorization of 17751 in exponential form is:

17751 = 31 × 611 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 17736 and 17751.

LCM(17736,17751) = 23 × 31 × 7391 × 611 × 971
LCM(17736,17751) = 104943912