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What is the Least Common Multiple of 6405 and 6419?

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 6405 and 6419 is 5873385.

LCM(6405,6419) = 5873385

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Least Common Multiple of 6405 and 6419 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6405 and 6419, than apply into the LCM equation.

GCF(6405,6419) = 7
LCM(6405,6419) = ( 6405 × 6419) / 7
LCM(6405,6419) = 41113695 / 7
LCM(6405,6419) = 5873385

Least Common Multiple (LCM) of 6405 and 6419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6405 and 6419. First we will calculate the prime factors of 6405 and 6419.

Prime Factorization of 6405

Prime factors of 6405 are 3, 5, 7, 61. Prime factorization of 6405 in exponential form is:

6405 = 31 × 51 × 71 × 611

Prime Factorization of 6419

Prime factors of 6419 are 7, 131. Prime factorization of 6419 in exponential form is:

6419 = 72 × 1311

Now multiplying the highest exponent prime factors to calculate the LCM of 6405 and 6419.

LCM(6405,6419) = 31 × 51 × 72 × 611 × 1311
LCM(6405,6419) = 5873385