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What is the Least Common Multiple of 8409 and 8414?

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 8409 and 8414 is 70753326.

LCM(8409,8414) = 70753326

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Least Common Multiple of 8409 and 8414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8409 and 8414, than apply into the LCM equation.

GCF(8409,8414) = 1
LCM(8409,8414) = ( 8409 × 8414) / 1
LCM(8409,8414) = 70753326 / 1
LCM(8409,8414) = 70753326

Least Common Multiple (LCM) of 8409 and 8414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8409 and 8414. First we will calculate the prime factors of 8409 and 8414.

Prime Factorization of 8409

Prime factors of 8409 are 3, 2803. Prime factorization of 8409 in exponential form is:

8409 = 31 × 28031

Prime Factorization of 8414

Prime factors of 8414 are 2, 7, 601. Prime factorization of 8414 in exponential form is:

8414 = 21 × 71 × 6011

Now multiplying the highest exponent prime factors to calculate the LCM of 8409 and 8414.

LCM(8409,8414) = 31 × 28031 × 21 × 71 × 6011
LCM(8409,8414) = 70753326