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What is the Least Common Multiple of 9693 and 9705?

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 9693 and 9705 is 31356855.

LCM(9693,9705) = 31356855

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Least Common Multiple of 9693 and 9705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9693 and 9705, than apply into the LCM equation.

GCF(9693,9705) = 3
LCM(9693,9705) = ( 9693 × 9705) / 3
LCM(9693,9705) = 94070565 / 3
LCM(9693,9705) = 31356855

Least Common Multiple (LCM) of 9693 and 9705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9693 and 9705. First we will calculate the prime factors of 9693 and 9705.

Prime Factorization of 9693

Prime factors of 9693 are 3, 359. Prime factorization of 9693 in exponential form is:

9693 = 33 × 3591

Prime Factorization of 9705

Prime factors of 9705 are 3, 5, 647. Prime factorization of 9705 in exponential form is:

9705 = 31 × 51 × 6471

Now multiplying the highest exponent prime factors to calculate the LCM of 9693 and 9705.

LCM(9693,9705) = 33 × 3591 × 51 × 6471
LCM(9693,9705) = 31356855