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What is the Least Common Multiple of 8064 and 8080?

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 8064 and 8080 is 4072320.

LCM(8064,8080) = 4072320

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Least Common Multiple of 8064 and 8080 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8064 and 8080, than apply into the LCM equation.

GCF(8064,8080) = 16
LCM(8064,8080) = ( 8064 × 8080) / 16
LCM(8064,8080) = 65157120 / 16
LCM(8064,8080) = 4072320

Least Common Multiple (LCM) of 8064 and 8080 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8064 and 8080. First we will calculate the prime factors of 8064 and 8080.

Prime Factorization of 8064

Prime factors of 8064 are 2, 3, 7. Prime factorization of 8064 in exponential form is:

8064 = 27 × 32 × 71

Prime Factorization of 8080

Prime factors of 8080 are 2, 5, 101. Prime factorization of 8080 in exponential form is:

8080 = 24 × 51 × 1011

Now multiplying the highest exponent prime factors to calculate the LCM of 8064 and 8080.

LCM(8064,8080) = 27 × 32 × 71 × 51 × 1011
LCM(8064,8080) = 4072320