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What is the Least Common Multiple of 65874 and 65880?

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 65874 and 65880 is 723296520.

LCM(65874,65880) = 723296520

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Least Common Multiple of 65874 and 65880 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65874 and 65880, than apply into the LCM equation.

GCF(65874,65880) = 6
LCM(65874,65880) = ( 65874 × 65880) / 6
LCM(65874,65880) = 4339779120 / 6
LCM(65874,65880) = 723296520

Least Common Multiple (LCM) of 65874 and 65880 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65874 and 65880. First we will calculate the prime factors of 65874 and 65880.

Prime Factorization of 65874

Prime factors of 65874 are 2, 3, 10979. Prime factorization of 65874 in exponential form is:

65874 = 21 × 31 × 109791

Prime Factorization of 65880

Prime factors of 65880 are 2, 3, 5, 61. Prime factorization of 65880 in exponential form is:

65880 = 23 × 33 × 51 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 65874 and 65880.

LCM(65874,65880) = 23 × 33 × 109791 × 51 × 611
LCM(65874,65880) = 723296520