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What is the Least Common Multiple of 17719 and 17734?

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 17719 and 17734 is 314228746.

LCM(17719,17734) = 314228746

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Least Common Multiple of 17719 and 17734 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17719 and 17734, than apply into the LCM equation.

GCF(17719,17734) = 1
LCM(17719,17734) = ( 17719 × 17734) / 1
LCM(17719,17734) = 314228746 / 1
LCM(17719,17734) = 314228746

Least Common Multiple (LCM) of 17719 and 17734 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17719 and 17734. First we will calculate the prime factors of 17719 and 17734.

Prime Factorization of 17719

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

17719 = 131 × 291 × 471

Prime Factorization of 17734

Prime factors of 17734 are 2, 8867. Prime factorization of 17734 in exponential form is:

17734 = 21 × 88671

Now multiplying the highest exponent prime factors to calculate the LCM of 17719 and 17734.

LCM(17719,17734) = 131 × 291 × 471 × 21 × 88671
LCM(17719,17734) = 314228746