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What is the Least Common Multiple of 17976 and 17988?

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 17976 and 17988 is 26946024.

LCM(17976,17988) = 26946024

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Least Common Multiple of 17976 and 17988 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17976 and 17988, than apply into the LCM equation.

GCF(17976,17988) = 12
LCM(17976,17988) = ( 17976 × 17988) / 12
LCM(17976,17988) = 323352288 / 12
LCM(17976,17988) = 26946024

Least Common Multiple (LCM) of 17976 and 17988 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17976 and 17988. First we will calculate the prime factors of 17976 and 17988.

Prime Factorization of 17976

Prime factors of 17976 are 2, 3, 7, 107. Prime factorization of 17976 in exponential form is:

17976 = 23 × 31 × 71 × 1071

Prime Factorization of 17988

Prime factors of 17988 are 2, 3, 1499. Prime factorization of 17988 in exponential form is:

17988 = 22 × 31 × 14991

Now multiplying the highest exponent prime factors to calculate the LCM of 17976 and 17988.

LCM(17976,17988) = 23 × 31 × 71 × 1071 × 14991
LCM(17976,17988) = 26946024