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What is the Least Common Multiple of 17850 and 17870?

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 17850 and 17870 is 31897950.

LCM(17850,17870) = 31897950

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Least Common Multiple of 17850 and 17870 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17850 and 17870, than apply into the LCM equation.

GCF(17850,17870) = 10
LCM(17850,17870) = ( 17850 × 17870) / 10
LCM(17850,17870) = 318979500 / 10
LCM(17850,17870) = 31897950

Least Common Multiple (LCM) of 17850 and 17870 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17850 and 17870. First we will calculate the prime factors of 17850 and 17870.

Prime Factorization of 17850

Prime factors of 17850 are 2, 3, 5, 7, 17. Prime factorization of 17850 in exponential form is:

17850 = 21 × 31 × 52 × 71 × 171

Prime Factorization of 17870

Prime factors of 17870 are 2, 5, 1787. Prime factorization of 17870 in exponential form is:

17870 = 21 × 51 × 17871

Now multiplying the highest exponent prime factors to calculate the LCM of 17850 and 17870.

LCM(17850,17870) = 21 × 31 × 52 × 71 × 171 × 17871
LCM(17850,17870) = 31897950