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What is the Least Common Multiple of 17875 and 17889?

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 17875 and 17889 is 319765875.

LCM(17875,17889) = 319765875

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Least Common Multiple of 17875 and 17889 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17875 and 17889, than apply into the LCM equation.

GCF(17875,17889) = 1
LCM(17875,17889) = ( 17875 × 17889) / 1
LCM(17875,17889) = 319765875 / 1
LCM(17875,17889) = 319765875

Least Common Multiple (LCM) of 17875 and 17889 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17875 and 17889. First we will calculate the prime factors of 17875 and 17889.

Prime Factorization of 17875

Prime factors of 17875 are 5, 11, 13. Prime factorization of 17875 in exponential form is:

17875 = 53 × 111 × 131

Prime Factorization of 17889

Prime factors of 17889 are 3, 67, 89. Prime factorization of 17889 in exponential form is:

17889 = 31 × 671 × 891

Now multiplying the highest exponent prime factors to calculate the LCM of 17875 and 17889.

LCM(17875,17889) = 53 × 111 × 131 × 31 × 671 × 891
LCM(17875,17889) = 319765875