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What is the Least Common Multiple of 65705 and 65720?

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 65705 and 65720 is 863626520.

LCM(65705,65720) = 863626520

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Least Common Multiple of 65705 and 65720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65705 and 65720, than apply into the LCM equation.

GCF(65705,65720) = 5
LCM(65705,65720) = ( 65705 × 65720) / 5
LCM(65705,65720) = 4318132600 / 5
LCM(65705,65720) = 863626520

Least Common Multiple (LCM) of 65705 and 65720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65705 and 65720. First we will calculate the prime factors of 65705 and 65720.

Prime Factorization of 65705

Prime factors of 65705 are 5, 17, 773. Prime factorization of 65705 in exponential form is:

65705 = 51 × 171 × 7731

Prime Factorization of 65720

Prime factors of 65720 are 2, 5, 31, 53. Prime factorization of 65720 in exponential form is:

65720 = 23 × 51 × 311 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 65705 and 65720.

LCM(65705,65720) = 51 × 171 × 7731 × 23 × 311 × 531
LCM(65705,65720) = 863626520