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What is the Least Common Multiple of 18700 and 18705?

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 18700 and 18705 is 69956700.

LCM(18700,18705) = 69956700

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Least Common Multiple of 18700 and 18705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18700 and 18705, than apply into the LCM equation.

GCF(18700,18705) = 5
LCM(18700,18705) = ( 18700 × 18705) / 5
LCM(18700,18705) = 349783500 / 5
LCM(18700,18705) = 69956700

Least Common Multiple (LCM) of 18700 and 18705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18700 and 18705. First we will calculate the prime factors of 18700 and 18705.

Prime Factorization of 18700

Prime factors of 18700 are 2, 5, 11, 17. Prime factorization of 18700 in exponential form is:

18700 = 22 × 52 × 111 × 171

Prime Factorization of 18705

Prime factors of 18705 are 3, 5, 29, 43. Prime factorization of 18705 in exponential form is:

18705 = 31 × 51 × 291 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 18700 and 18705.

LCM(18700,18705) = 22 × 52 × 111 × 171 × 31 × 291 × 431
LCM(18700,18705) = 69956700