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What is the Least Common Multiple of 10311 and 10320?

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 10311 and 10320 is 35469840.

LCM(10311,10320) = 35469840

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Least Common Multiple of 10311 and 10320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10311 and 10320, than apply into the LCM equation.

GCF(10311,10320) = 3
LCM(10311,10320) = ( 10311 × 10320) / 3
LCM(10311,10320) = 106409520 / 3
LCM(10311,10320) = 35469840

Least Common Multiple (LCM) of 10311 and 10320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10311 and 10320. First we will calculate the prime factors of 10311 and 10320.

Prime Factorization of 10311

Prime factors of 10311 are 3, 7, 491. Prime factorization of 10311 in exponential form is:

10311 = 31 × 71 × 4911

Prime Factorization of 10320

Prime factors of 10320 are 2, 3, 5, 43. Prime factorization of 10320 in exponential form is:

10320 = 24 × 31 × 51 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 10311 and 10320.

LCM(10311,10320) = 31 × 71 × 4911 × 24 × 51 × 431
LCM(10311,10320) = 35469840