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What is the Least Common Multiple of 1405 and 1409?

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 1405 and 1409 is 1979645.

LCM(1405,1409) = 1979645

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Least Common Multiple of 1405 and 1409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1405 and 1409, than apply into the LCM equation.

GCF(1405,1409) = 1
LCM(1405,1409) = ( 1405 × 1409) / 1
LCM(1405,1409) = 1979645 / 1
LCM(1405,1409) = 1979645

Least Common Multiple (LCM) of 1405 and 1409 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1405 and 1409. First we will calculate the prime factors of 1405 and 1409.

Prime Factorization of 1405

Prime factors of 1405 are 5, 281. Prime factorization of 1405 in exponential form is:

1405 = 51 × 2811

Prime Factorization of 1409

Prime factors of 1409 are 1409. Prime factorization of 1409 in exponential form is:

1409 = 14091

Now multiplying the highest exponent prime factors to calculate the LCM of 1405 and 1409.

LCM(1405,1409) = 51 × 2811 × 14091
LCM(1405,1409) = 1979645