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What is the Least Common Multiple of 18100 and 18109?

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 18100 and 18109 is 327772900.

LCM(18100,18109) = 327772900

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Least Common Multiple of 18100 and 18109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18100 and 18109, than apply into the LCM equation.

GCF(18100,18109) = 1
LCM(18100,18109) = ( 18100 × 18109) / 1
LCM(18100,18109) = 327772900 / 1
LCM(18100,18109) = 327772900

Least Common Multiple (LCM) of 18100 and 18109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18100 and 18109. First we will calculate the prime factors of 18100 and 18109.

Prime Factorization of 18100

Prime factors of 18100 are 2, 5, 181. Prime factorization of 18100 in exponential form is:

18100 = 22 × 52 × 1811

Prime Factorization of 18109

Prime factors of 18109 are 7, 13, 199. Prime factorization of 18109 in exponential form is:

18109 = 71 × 131 × 1991

Now multiplying the highest exponent prime factors to calculate the LCM of 18100 and 18109.

LCM(18100,18109) = 22 × 52 × 1811 × 71 × 131 × 1991
LCM(18100,18109) = 327772900