What is the Least Common Multiple of 12004 and 12008?
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 12004 and 12008 is 36036008.
LCM(12004,12008) = 36036008
Least Common Multiple of 12004 and 12008 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12004 and 12008, than apply into the LCM equation.
GCF(12004,12008) = 4
LCM(12004,12008) = ( 12004 × 12008) / 4
LCM(12004,12008) = 144144032 / 4
LCM(12004,12008) = 36036008
Least Common Multiple (LCM) of 12004 and 12008 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 12004 and 12008. First we will calculate the prime factors of 12004 and 12008.
Prime Factorization of 12004
Prime factors of 12004 are 2, 3001. Prime factorization of 12004 in exponential form is:
12004 = 22 × 30011
Prime Factorization of 12008
Prime factors of 12008 are 2, 19, 79. Prime factorization of 12008 in exponential form is:
12008 = 23 × 191 × 791
Now multiplying the highest exponent prime factors to calculate the LCM of 12004 and 12008.
LCM(12004,12008) = 23 × 30011 × 191 × 791
LCM(12004,12008) = 36036008
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