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What is the Least Common Multiple of 65760 and 65764?

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 65764 is 1081160160.

LCM(65760,65764) = 1081160160

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Least Common Multiple of 65760 and 65764 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 65764, than apply into the LCM equation.

GCF(65760,65764) = 4
LCM(65760,65764) = ( 65760 × 65764) / 4
LCM(65760,65764) = 4324640640 / 4
LCM(65760,65764) = 1081160160

Least Common Multiple (LCM) of 65760 and 65764 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65760 and 65764. First we will calculate the prime factors of 65760 and 65764.

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 65764

Prime factors of 65764 are 2, 41, 401. Prime factorization of 65764 in exponential form is:

65764 = 22 × 411 × 4011

Now multiplying the highest exponent prime factors to calculate the LCM of 65760 and 65764.

LCM(65760,65764) = 25 × 31 × 51 × 1371 × 411 × 4011
LCM(65760,65764) = 1081160160