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What is the Least Common Multiple of 11688 and 11700?

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 11688 and 11700 is 11395800.

LCM(11688,11700) = 11395800

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Least Common Multiple of 11688 and 11700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 11688 and 11700, than apply into the LCM equation.

GCF(11688,11700) = 12
LCM(11688,11700) = ( 11688 × 11700) / 12
LCM(11688,11700) = 136749600 / 12
LCM(11688,11700) = 11395800

Least Common Multiple (LCM) of 11688 and 11700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 11688 and 11700. First we will calculate the prime factors of 11688 and 11700.

Prime Factorization of 11688

Prime factors of 11688 are 2, 3, 487. Prime factorization of 11688 in exponential form is:

11688 = 23 × 31 × 4871

Prime Factorization of 11700

Prime factors of 11700 are 2, 3, 5, 13. Prime factorization of 11700 in exponential form is:

11700 = 22 × 32 × 52 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 11688 and 11700.

LCM(11688,11700) = 23 × 32 × 4871 × 52 × 131
LCM(11688,11700) = 11395800