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What is the Least Common Multiple of 17709 and 17719?

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 17709 and 17719 is 313785771.

LCM(17709,17719) = 313785771

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Least Common Multiple of 17709 and 17719 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17709 and 17719, than apply into the LCM equation.

GCF(17709,17719) = 1
LCM(17709,17719) = ( 17709 × 17719) / 1
LCM(17709,17719) = 313785771 / 1
LCM(17709,17719) = 313785771

Least Common Multiple (LCM) of 17709 and 17719 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17709 and 17719. First we will calculate the prime factors of 17709 and 17719.

Prime Factorization of 17709

Prime factors of 17709 are 3, 5903. Prime factorization of 17709 in exponential form is:

17709 = 31 × 59031

Prime Factorization of 17719

Prime factors of 17719 are 13, 29, 47. Prime factorization of 17719 in exponential form is:

17719 = 131 × 291 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 17709 and 17719.

LCM(17709,17719) = 31 × 59031 × 131 × 291 × 471
LCM(17709,17719) = 313785771