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What is the Least Common Multiple of 17854 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 17854 and 17870 is 159525490.

LCM(17854,17870) = 159525490

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Least Common Multiple of 17854 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 17854 and 17870, than apply into the LCM equation.

GCF(17854,17870) = 2
LCM(17854,17870) = ( 17854 × 17870) / 2
LCM(17854,17870) = 319050980 / 2
LCM(17854,17870) = 159525490

Least Common Multiple (LCM) of 17854 and 17870 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17854 and 17870. First we will calculate the prime factors of 17854 and 17870.

Prime Factorization of 17854

Prime factors of 17854 are 2, 79, 113. Prime factorization of 17854 in exponential form is:

17854 = 21 × 791 × 1131

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 17854 and 17870.

LCM(17854,17870) = 21 × 791 × 1131 × 51 × 17871
LCM(17854,17870) = 159525490