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What is the Least Common Multiple of 8140 and 8160?

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 8140 and 8160 is 3321120.

LCM(8140,8160) = 3321120

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Least Common Multiple of 8140 and 8160 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8140 and 8160, than apply into the LCM equation.

GCF(8140,8160) = 20
LCM(8140,8160) = ( 8140 × 8160) / 20
LCM(8140,8160) = 66422400 / 20
LCM(8140,8160) = 3321120

Least Common Multiple (LCM) of 8140 and 8160 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8140 and 8160. First we will calculate the prime factors of 8140 and 8160.

Prime Factorization of 8140

Prime factors of 8140 are 2, 5, 11, 37. Prime factorization of 8140 in exponential form is:

8140 = 22 × 51 × 111 × 371

Prime Factorization of 8160

Prime factors of 8160 are 2, 3, 5, 17. Prime factorization of 8160 in exponential form is:

8160 = 25 × 31 × 51 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 8140 and 8160.

LCM(8140,8160) = 25 × 51 × 111 × 371 × 31 × 171
LCM(8140,8160) = 3321120