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What is the Least Common Multiple of 8040 and 8049?

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 8040 and 8049 is 21571320.

LCM(8040,8049) = 21571320

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Least Common Multiple of 8040 and 8049 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8040 and 8049, than apply into the LCM equation.

GCF(8040,8049) = 3
LCM(8040,8049) = ( 8040 × 8049) / 3
LCM(8040,8049) = 64713960 / 3
LCM(8040,8049) = 21571320

Least Common Multiple (LCM) of 8040 and 8049 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8040 and 8049. First we will calculate the prime factors of 8040 and 8049.

Prime Factorization of 8040

Prime factors of 8040 are 2, 3, 5, 67. Prime factorization of 8040 in exponential form is:

8040 = 23 × 31 × 51 × 671

Prime Factorization of 8049

Prime factors of 8049 are 3, 2683. Prime factorization of 8049 in exponential form is:

8049 = 31 × 26831

Now multiplying the highest exponent prime factors to calculate the LCM of 8040 and 8049.

LCM(8040,8049) = 23 × 31 × 51 × 671 × 26831
LCM(8040,8049) = 21571320