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What is the Least Common Multiple of 65505 and 65514?

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 65505 and 65514 is 1430498190.

LCM(65505,65514) = 1430498190

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Least Common Multiple of 65505 and 65514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65505 and 65514, than apply into the LCM equation.

GCF(65505,65514) = 3
LCM(65505,65514) = ( 65505 × 65514) / 3
LCM(65505,65514) = 4291494570 / 3
LCM(65505,65514) = 1430498190

Least Common Multiple (LCM) of 65505 and 65514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65505 and 65514. First we will calculate the prime factors of 65505 and 65514.

Prime Factorization of 65505

Prime factors of 65505 are 3, 5, 11, 397. Prime factorization of 65505 in exponential form is:

65505 = 31 × 51 × 111 × 3971

Prime Factorization of 65514

Prime factors of 65514 are 2, 3, 61, 179. Prime factorization of 65514 in exponential form is:

65514 = 21 × 31 × 611 × 1791

Now multiplying the highest exponent prime factors to calculate the LCM of 65505 and 65514.

LCM(65505,65514) = 31 × 51 × 111 × 3971 × 21 × 611 × 1791
LCM(65505,65514) = 1430498190