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What is the Least Common Multiple of 16680 and 16700?

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 16680 and 16700 is 13927800.

LCM(16680,16700) = 13927800

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Least Common Multiple of 16680 and 16700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16680 and 16700, than apply into the LCM equation.

GCF(16680,16700) = 20
LCM(16680,16700) = ( 16680 × 16700) / 20
LCM(16680,16700) = 278556000 / 20
LCM(16680,16700) = 13927800

Least Common Multiple (LCM) of 16680 and 16700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16680 and 16700. First we will calculate the prime factors of 16680 and 16700.

Prime Factorization of 16680

Prime factors of 16680 are 2, 3, 5, 139. Prime factorization of 16680 in exponential form is:

16680 = 23 × 31 × 51 × 1391

Prime Factorization of 16700

Prime factors of 16700 are 2, 5, 167. Prime factorization of 16700 in exponential form is:

16700 = 22 × 52 × 1671

Now multiplying the highest exponent prime factors to calculate the LCM of 16680 and 16700.

LCM(16680,16700) = 23 × 31 × 52 × 1391 × 1671
LCM(16680,16700) = 13927800