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What is the Least Common Multiple of 1690 and 1709?

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 1690 and 1709 is 2888210.

LCM(1690,1709) = 2888210

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Least Common Multiple of 1690 and 1709 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1690 and 1709, than apply into the LCM equation.

GCF(1690,1709) = 1
LCM(1690,1709) = ( 1690 × 1709) / 1
LCM(1690,1709) = 2888210 / 1
LCM(1690,1709) = 2888210

Least Common Multiple (LCM) of 1690 and 1709 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1690 and 1709. First we will calculate the prime factors of 1690 and 1709.

Prime Factorization of 1690

Prime factors of 1690 are 2, 5, 13. Prime factorization of 1690 in exponential form is:

1690 = 21 × 51 × 132

Prime Factorization of 1709

Prime factors of 1709 are 1709. Prime factorization of 1709 in exponential form is:

1709 = 17091

Now multiplying the highest exponent prime factors to calculate the LCM of 1690 and 1709.

LCM(1690,1709) = 21 × 51 × 132 × 17091
LCM(1690,1709) = 2888210