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What is the Least Common Multiple of 65760 and 65768?

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 65760 and 65768 is 540612960.

LCM(65760,65768) = 540612960

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Least Common Multiple of 65760 and 65768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65760 and 65768, than apply into the LCM equation.

GCF(65760,65768) = 8
LCM(65760,65768) = ( 65760 × 65768) / 8
LCM(65760,65768) = 4324903680 / 8
LCM(65760,65768) = 540612960

Least Common Multiple (LCM) of 65760 and 65768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65760 and 65768. First we will calculate the prime factors of 65760 and 65768.

Prime Factorization of 65760

Prime factors of 65760 are 2, 3, 5, 137. Prime factorization of 65760 in exponential form is:

65760 = 25 × 31 × 51 × 1371

Prime Factorization of 65768

Prime factors of 65768 are 2, 8221. Prime factorization of 65768 in exponential form is:

65768 = 23 × 82211

Now multiplying the highest exponent prime factors to calculate the LCM of 65760 and 65768.

LCM(65760,65768) = 25 × 31 × 51 × 1371 × 82211
LCM(65760,65768) = 540612960