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What is the Least Common Multiple of 18105 and 18110?

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 18105 and 18110 is 65576310.

LCM(18105,18110) = 65576310

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Least Common Multiple of 18105 and 18110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18105 and 18110, than apply into the LCM equation.

GCF(18105,18110) = 5
LCM(18105,18110) = ( 18105 × 18110) / 5
LCM(18105,18110) = 327881550 / 5
LCM(18105,18110) = 65576310

Least Common Multiple (LCM) of 18105 and 18110 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18105 and 18110. First we will calculate the prime factors of 18105 and 18110.

Prime Factorization of 18105

Prime factors of 18105 are 3, 5, 17, 71. Prime factorization of 18105 in exponential form is:

18105 = 31 × 51 × 171 × 711

Prime Factorization of 18110

Prime factors of 18110 are 2, 5, 1811. Prime factorization of 18110 in exponential form is:

18110 = 21 × 51 × 18111

Now multiplying the highest exponent prime factors to calculate the LCM of 18105 and 18110.

LCM(18105,18110) = 31 × 51 × 171 × 711 × 21 × 18111
LCM(18105,18110) = 65576310