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What is the Least Common Multiple of 12699 and 12705?

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 12699 and 12705 is 53780265.

LCM(12699,12705) = 53780265

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Least Common Multiple of 12699 and 12705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12699 and 12705, than apply into the LCM equation.

GCF(12699,12705) = 3
LCM(12699,12705) = ( 12699 × 12705) / 3
LCM(12699,12705) = 161340795 / 3
LCM(12699,12705) = 53780265

Least Common Multiple (LCM) of 12699 and 12705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12699 and 12705. First we will calculate the prime factors of 12699 and 12705.

Prime Factorization of 12699

Prime factors of 12699 are 3, 17, 83. Prime factorization of 12699 in exponential form is:

12699 = 32 × 171 × 831

Prime Factorization of 12705

Prime factors of 12705 are 3, 5, 7, 11. Prime factorization of 12705 in exponential form is:

12705 = 31 × 51 × 71 × 112

Now multiplying the highest exponent prime factors to calculate the LCM of 12699 and 12705.

LCM(12699,12705) = 32 × 171 × 831 × 51 × 71 × 112
LCM(12699,12705) = 53780265