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What is the Least Common Multiple of 1095 and 1110?

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 1095 and 1110 is 81030.

LCM(1095,1110) = 81030

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Least Common Multiple of 1095 and 1110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1095 and 1110, than apply into the LCM equation.

GCF(1095,1110) = 15
LCM(1095,1110) = ( 1095 × 1110) / 15
LCM(1095,1110) = 1215450 / 15
LCM(1095,1110) = 81030

Least Common Multiple (LCM) of 1095 and 1110 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1095 and 1110. First we will calculate the prime factors of 1095 and 1110.

Prime Factorization of 1095

Prime factors of 1095 are 3, 5, 73. Prime factorization of 1095 in exponential form is:

1095 = 31 × 51 × 731

Prime Factorization of 1110

Prime factors of 1110 are 2, 3, 5, 37. Prime factorization of 1110 in exponential form is:

1110 = 21 × 31 × 51 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 1095 and 1110.

LCM(1095,1110) = 31 × 51 × 731 × 21 × 371
LCM(1095,1110) = 81030