What is the Least Common Multiple of 2009 and 2016?
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 2009 and 2016 is 578592.
LCM(2009,2016) = 578592
Least Common Multiple of 2009 and 2016 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2009 and 2016, than apply into the LCM equation.
GCF(2009,2016) = 7
LCM(2009,2016) = ( 2009 × 2016) / 7
LCM(2009,2016) = 4050144 / 7
LCM(2009,2016) = 578592
Least Common Multiple (LCM) of 2009 and 2016 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 2009 and 2016. First we will calculate the prime factors of 2009 and 2016.
Prime Factorization of 2009
Prime factors of 2009 are 7, 41. Prime factorization of 2009 in exponential form is:
2009 = 72 × 411
Prime Factorization of 2016
Prime factors of 2016 are 2, 3, 7. Prime factorization of 2016 in exponential form is:
2016 = 25 × 32 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 2009 and 2016.
LCM(2009,2016) = 72 × 411 × 25 × 32
LCM(2009,2016) = 578592
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