What is the Least Common Multiple of 8005 and 8024?
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 8005 and 8024 is 64232120.
LCM(8005,8024) = 64232120
Least Common Multiple of 8005 and 8024 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8005 and 8024, than apply into the LCM equation.
GCF(8005,8024) = 1
LCM(8005,8024) = ( 8005 × 8024) / 1
LCM(8005,8024) = 64232120 / 1
LCM(8005,8024) = 64232120
Least Common Multiple (LCM) of 8005 and 8024 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 8005 and 8024. First we will calculate the prime factors of 8005 and 8024.
Prime Factorization of 8005
Prime factors of 8005 are 5, 1601. Prime factorization of 8005 in exponential form is:
8005 = 51 × 16011
Prime Factorization of 8024
Prime factors of 8024 are 2, 17, 59. Prime factorization of 8024 in exponential form is:
8024 = 23 × 171 × 591
Now multiplying the highest exponent prime factors to calculate the LCM of 8005 and 8024.
LCM(8005,8024) = 51 × 16011 × 23 × 171 × 591
LCM(8005,8024) = 64232120
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