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What is the Least Common Multiple of 10731 and 10740?

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 10731 and 10740 is 38416980.

LCM(10731,10740) = 38416980

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Least Common Multiple of 10731 and 10740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10731 and 10740, than apply into the LCM equation.

GCF(10731,10740) = 3
LCM(10731,10740) = ( 10731 × 10740) / 3
LCM(10731,10740) = 115250940 / 3
LCM(10731,10740) = 38416980

Least Common Multiple (LCM) of 10731 and 10740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10731 and 10740. First we will calculate the prime factors of 10731 and 10740.

Prime Factorization of 10731

Prime factors of 10731 are 3, 7, 73. Prime factorization of 10731 in exponential form is:

10731 = 31 × 72 × 731

Prime Factorization of 10740

Prime factors of 10740 are 2, 3, 5, 179. Prime factorization of 10740 in exponential form is:

10740 = 22 × 31 × 51 × 1791

Now multiplying the highest exponent prime factors to calculate the LCM of 10731 and 10740.

LCM(10731,10740) = 31 × 72 × 731 × 22 × 51 × 1791
LCM(10731,10740) = 38416980