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What is the Least Common Multiple of 1682 and 1690?

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 1682 and 1690 is 1421290.

LCM(1682,1690) = 1421290

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Least Common Multiple of 1682 and 1690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1682 and 1690, than apply into the LCM equation.

GCF(1682,1690) = 2
LCM(1682,1690) = ( 1682 × 1690) / 2
LCM(1682,1690) = 2842580 / 2
LCM(1682,1690) = 1421290

Least Common Multiple (LCM) of 1682 and 1690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1682 and 1690. First we will calculate the prime factors of 1682 and 1690.

Prime Factorization of 1682

Prime factors of 1682 are 2, 29. Prime factorization of 1682 in exponential form is:

1682 = 21 × 292

Prime Factorization of 1690

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

1690 = 21 × 51 × 132

Now multiplying the highest exponent prime factors to calculate the LCM of 1682 and 1690.

LCM(1682,1690) = 21 × 292 × 51 × 132
LCM(1682,1690) = 1421290