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What is the Least Common Multiple of 17751 and 17768?

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 17751 and 17768 is 315399768.

LCM(17751,17768) = 315399768

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Least Common Multiple of 17751 and 17768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17751 and 17768, than apply into the LCM equation.

GCF(17751,17768) = 1
LCM(17751,17768) = ( 17751 × 17768) / 1
LCM(17751,17768) = 315399768 / 1
LCM(17751,17768) = 315399768

Least Common Multiple (LCM) of 17751 and 17768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17751 and 17768. First we will calculate the prime factors of 17751 and 17768.

Prime Factorization of 17751

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

17751 = 31 × 611 × 971

Prime Factorization of 17768

Prime factors of 17768 are 2, 2221. Prime factorization of 17768 in exponential form is:

17768 = 23 × 22211

Now multiplying the highest exponent prime factors to calculate the LCM of 17751 and 17768.

LCM(17751,17768) = 31 × 611 × 971 × 23 × 22211
LCM(17751,17768) = 315399768