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What is the Least Common Multiple of 12048 and 12065?

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 12048 and 12065 is 145359120.

LCM(12048,12065) = 145359120

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Least Common Multiple of 12048 and 12065 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12048 and 12065, than apply into the LCM equation.

GCF(12048,12065) = 1
LCM(12048,12065) = ( 12048 × 12065) / 1
LCM(12048,12065) = 145359120 / 1
LCM(12048,12065) = 145359120

Least Common Multiple (LCM) of 12048 and 12065 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12048 and 12065. First we will calculate the prime factors of 12048 and 12065.

Prime Factorization of 12048

Prime factors of 12048 are 2, 3, 251. Prime factorization of 12048 in exponential form is:

12048 = 24 × 31 × 2511

Prime Factorization of 12065

Prime factors of 12065 are 5, 19, 127. Prime factorization of 12065 in exponential form is:

12065 = 51 × 191 × 1271

Now multiplying the highest exponent prime factors to calculate the LCM of 12048 and 12065.

LCM(12048,12065) = 24 × 31 × 2511 × 51 × 191 × 1271
LCM(12048,12065) = 145359120