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What is the Least Common Multiple of 810 and 829?

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 810 and 829 is 671490.

LCM(810,829) = 671490

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Least Common Multiple of 810 and 829 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 810 and 829, than apply into the LCM equation.

GCF(810,829) = 1
LCM(810,829) = ( 810 × 829) / 1
LCM(810,829) = 671490 / 1
LCM(810,829) = 671490

Least Common Multiple (LCM) of 810 and 829 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 810 and 829. First we will calculate the prime factors of 810 and 829.

Prime Factorization of 810

Prime factors of 810 are 2, 3, 5. Prime factorization of 810 in exponential form is:

810 = 21 × 34 × 51

Prime Factorization of 829

Prime factors of 829 are 829. Prime factorization of 829 in exponential form is:

829 = 8291

Now multiplying the highest exponent prime factors to calculate the LCM of 810 and 829.

LCM(810,829) = 21 × 34 × 51 × 8291
LCM(810,829) = 671490