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What is the Least Common Multiple of 17752 and 17759?

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 17752 and 17759 is 45036824.

LCM(17752,17759) = 45036824

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Least Common Multiple of 17752 and 17759 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17752 and 17759, than apply into the LCM equation.

GCF(17752,17759) = 7
LCM(17752,17759) = ( 17752 × 17759) / 7
LCM(17752,17759) = 315257768 / 7
LCM(17752,17759) = 45036824

Least Common Multiple (LCM) of 17752 and 17759 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17752 and 17759. First we will calculate the prime factors of 17752 and 17759.

Prime Factorization of 17752

Prime factors of 17752 are 2, 7, 317. Prime factorization of 17752 in exponential form is:

17752 = 23 × 71 × 3171

Prime Factorization of 17759

Prime factors of 17759 are 7, 43, 59. Prime factorization of 17759 in exponential form is:

17759 = 71 × 431 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 17752 and 17759.

LCM(17752,17759) = 23 × 71 × 3171 × 431 × 591
LCM(17752,17759) = 45036824