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What is the Least Common Multiple of 12012 and 12032?

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 12012 and 12032 is 36132096.

LCM(12012,12032) = 36132096

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Least Common Multiple of 12012 and 12032 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12012 and 12032, than apply into the LCM equation.

GCF(12012,12032) = 4
LCM(12012,12032) = ( 12012 × 12032) / 4
LCM(12012,12032) = 144528384 / 4
LCM(12012,12032) = 36132096

Least Common Multiple (LCM) of 12012 and 12032 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12012 and 12032. First we will calculate the prime factors of 12012 and 12032.

Prime Factorization of 12012

Prime factors of 12012 are 2, 3, 7, 11, 13. Prime factorization of 12012 in exponential form is:

12012 = 22 × 31 × 71 × 111 × 131

Prime Factorization of 12032

Prime factors of 12032 are 2, 47. Prime factorization of 12032 in exponential form is:

12032 = 28 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 12012 and 12032.

LCM(12012,12032) = 28 × 31 × 71 × 111 × 131 × 471
LCM(12012,12032) = 36132096