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What is the Least Common Multiple of 1110 and 1116?

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 1110 and 1116 is 206460.

LCM(1110,1116) = 206460

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Least Common Multiple of 1110 and 1116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1110 and 1116, than apply into the LCM equation.

GCF(1110,1116) = 6
LCM(1110,1116) = ( 1110 × 1116) / 6
LCM(1110,1116) = 1238760 / 6
LCM(1110,1116) = 206460

Least Common Multiple (LCM) of 1110 and 1116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1110 and 1116. First we will calculate the prime factors of 1110 and 1116.

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

Prime Factorization of 1116

Prime factors of 1116 are 2, 3, 31. Prime factorization of 1116 in exponential form is:

1116 = 22 × 32 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 1110 and 1116.

LCM(1110,1116) = 22 × 32 × 51 × 371 × 311
LCM(1110,1116) = 206460