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What is the Least Common Multiple of 17800 and 17820?

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 17800 and 17820 is 15859800.

LCM(17800,17820) = 15859800

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Least Common Multiple of 17800 and 17820 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17800 and 17820, than apply into the LCM equation.

GCF(17800,17820) = 20
LCM(17800,17820) = ( 17800 × 17820) / 20
LCM(17800,17820) = 317196000 / 20
LCM(17800,17820) = 15859800

Least Common Multiple (LCM) of 17800 and 17820 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17800 and 17820. First we will calculate the prime factors of 17800 and 17820.

Prime Factorization of 17800

Prime factors of 17800 are 2, 5, 89. Prime factorization of 17800 in exponential form is:

17800 = 23 × 52 × 891

Prime Factorization of 17820

Prime factors of 17820 are 2, 3, 5, 11. Prime factorization of 17820 in exponential form is:

17820 = 22 × 34 × 51 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 17800 and 17820.

LCM(17800,17820) = 23 × 52 × 891 × 34 × 111
LCM(17800,17820) = 15859800