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What is the Least Common Multiple of 1683 and 1687?

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 1683 and 1687 is 2839221.

LCM(1683,1687) = 2839221

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Least Common Multiple of 1683 and 1687 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1683 and 1687, than apply into the LCM equation.

GCF(1683,1687) = 1
LCM(1683,1687) = ( 1683 × 1687) / 1
LCM(1683,1687) = 2839221 / 1
LCM(1683,1687) = 2839221

Least Common Multiple (LCM) of 1683 and 1687 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1683 and 1687. First we will calculate the prime factors of 1683 and 1687.

Prime Factorization of 1683

Prime factors of 1683 are 3, 11, 17. Prime factorization of 1683 in exponential form is:

1683 = 32 × 111 × 171

Prime Factorization of 1687

Prime factors of 1687 are 7, 241. Prime factorization of 1687 in exponential form is:

1687 = 71 × 2411

Now multiplying the highest exponent prime factors to calculate the LCM of 1683 and 1687.

LCM(1683,1687) = 32 × 111 × 171 × 71 × 2411
LCM(1683,1687) = 2839221