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What is the Least Common Multiple of 1409 and 1417?

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 1409 and 1417 is 1996553.

LCM(1409,1417) = 1996553

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Least Common Multiple of 1409 and 1417 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1409 and 1417, than apply into the LCM equation.

GCF(1409,1417) = 1
LCM(1409,1417) = ( 1409 × 1417) / 1
LCM(1409,1417) = 1996553 / 1
LCM(1409,1417) = 1996553

Least Common Multiple (LCM) of 1409 and 1417 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1409 and 1417. First we will calculate the prime factors of 1409 and 1417.

Prime Factorization of 1409

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

1409 = 14091

Prime Factorization of 1417

Prime factors of 1417 are 13, 109. Prime factorization of 1417 in exponential form is:

1417 = 131 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 1409 and 1417.

LCM(1409,1417) = 14091 × 131 × 1091
LCM(1409,1417) = 1996553