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What is the Least Common Multiple of 9969 and 9978?

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 9969 and 9978 is 33156894.

LCM(9969,9978) = 33156894

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Least Common Multiple of 9969 and 9978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9969 and 9978, than apply into the LCM equation.

GCF(9969,9978) = 3
LCM(9969,9978) = ( 9969 × 9978) / 3
LCM(9969,9978) = 99470682 / 3
LCM(9969,9978) = 33156894

Least Common Multiple (LCM) of 9969 and 9978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9969 and 9978. First we will calculate the prime factors of 9969 and 9978.

Prime Factorization of 9969

Prime factors of 9969 are 3, 3323. Prime factorization of 9969 in exponential form is:

9969 = 31 × 33231

Prime Factorization of 9978

Prime factors of 9978 are 2, 3, 1663. Prime factorization of 9978 in exponential form is:

9978 = 21 × 31 × 16631

Now multiplying the highest exponent prime factors to calculate the LCM of 9969 and 9978.

LCM(9969,9978) = 31 × 33231 × 21 × 16631
LCM(9969,9978) = 33156894