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What is the Least Common Multiple of 10405 and 10409?

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 10405 and 10409 is 108305645.

LCM(10405,10409) = 108305645

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Least Common Multiple of 10405 and 10409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10405 and 10409, than apply into the LCM equation.

GCF(10405,10409) = 1
LCM(10405,10409) = ( 10405 × 10409) / 1
LCM(10405,10409) = 108305645 / 1
LCM(10405,10409) = 108305645

Least Common Multiple (LCM) of 10405 and 10409 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10405 and 10409. First we will calculate the prime factors of 10405 and 10409.

Prime Factorization of 10405

Prime factors of 10405 are 5, 2081. Prime factorization of 10405 in exponential form is:

10405 = 51 × 20811

Prime Factorization of 10409

Prime factors of 10409 are 7, 1487. Prime factorization of 10409 in exponential form is:

10409 = 71 × 14871

Now multiplying the highest exponent prime factors to calculate the LCM of 10405 and 10409.

LCM(10405,10409) = 51 × 20811 × 71 × 14871
LCM(10405,10409) = 108305645