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What is the Least Common Multiple of 17900 and 17919?

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 17900 and 17919 is 320750100.

LCM(17900,17919) = 320750100

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Least Common Multiple of 17900 and 17919 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17900 and 17919, than apply into the LCM equation.

GCF(17900,17919) = 1
LCM(17900,17919) = ( 17900 × 17919) / 1
LCM(17900,17919) = 320750100 / 1
LCM(17900,17919) = 320750100

Least Common Multiple (LCM) of 17900 and 17919 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17900 and 17919. First we will calculate the prime factors of 17900 and 17919.

Prime Factorization of 17900

Prime factors of 17900 are 2, 5, 179. Prime factorization of 17900 in exponential form is:

17900 = 22 × 52 × 1791

Prime Factorization of 17919

Prime factors of 17919 are 3, 11, 181. Prime factorization of 17919 in exponential form is:

17919 = 32 × 111 × 1811

Now multiplying the highest exponent prime factors to calculate the LCM of 17900 and 17919.

LCM(17900,17919) = 22 × 52 × 1791 × 32 × 111 × 1811
LCM(17900,17919) = 320750100