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What is the Least Common Multiple of 9976 and 9988?

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 9976 and 9988 is 24910072.

LCM(9976,9988) = 24910072

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Least Common Multiple of 9976 and 9988 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9976 and 9988, than apply into the LCM equation.

GCF(9976,9988) = 4
LCM(9976,9988) = ( 9976 × 9988) / 4
LCM(9976,9988) = 99640288 / 4
LCM(9976,9988) = 24910072

Least Common Multiple (LCM) of 9976 and 9988 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9976 and 9988. First we will calculate the prime factors of 9976 and 9988.

Prime Factorization of 9976

Prime factors of 9976 are 2, 29, 43. Prime factorization of 9976 in exponential form is:

9976 = 23 × 291 × 431

Prime Factorization of 9988

Prime factors of 9988 are 2, 11, 227. Prime factorization of 9988 in exponential form is:

9988 = 22 × 111 × 2271

Now multiplying the highest exponent prime factors to calculate the LCM of 9976 and 9988.

LCM(9976,9988) = 23 × 291 × 431 × 111 × 2271
LCM(9976,9988) = 24910072