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What is the Least Common Multiple of 3405 and 3414?

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 3405 and 3414 is 3874890.

LCM(3405,3414) = 3874890

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Least Common Multiple of 3405 and 3414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3405 and 3414, than apply into the LCM equation.

GCF(3405,3414) = 3
LCM(3405,3414) = ( 3405 × 3414) / 3
LCM(3405,3414) = 11624670 / 3
LCM(3405,3414) = 3874890

Least Common Multiple (LCM) of 3405 and 3414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3405 and 3414. First we will calculate the prime factors of 3405 and 3414.

Prime Factorization of 3405

Prime factors of 3405 are 3, 5, 227. Prime factorization of 3405 in exponential form is:

3405 = 31 × 51 × 2271

Prime Factorization of 3414

Prime factors of 3414 are 2, 3, 569. Prime factorization of 3414 in exponential form is:

3414 = 21 × 31 × 5691

Now multiplying the highest exponent prime factors to calculate the LCM of 3405 and 3414.

LCM(3405,3414) = 31 × 51 × 2271 × 21 × 5691
LCM(3405,3414) = 3874890