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What is the Least Common Multiple of 1080 and 1085?

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 1080 and 1085 is 234360.

LCM(1080,1085) = 234360

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Least Common Multiple of 1080 and 1085 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1080 and 1085, than apply into the LCM equation.

GCF(1080,1085) = 5
LCM(1080,1085) = ( 1080 × 1085) / 5
LCM(1080,1085) = 1171800 / 5
LCM(1080,1085) = 234360

Least Common Multiple (LCM) of 1080 and 1085 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1080 and 1085. First we will calculate the prime factors of 1080 and 1085.

Prime Factorization of 1080

Prime factors of 1080 are 2, 3, 5. Prime factorization of 1080 in exponential form is:

1080 = 23 × 33 × 51

Prime Factorization of 1085

Prime factors of 1085 are 5, 7, 31. Prime factorization of 1085 in exponential form is:

1085 = 51 × 71 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 1080 and 1085.

LCM(1080,1085) = 23 × 33 × 51 × 71 × 311
LCM(1080,1085) = 234360