What is the Least Common Multiple of 67004 and 67008?
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 67004 and 67008 is 1122451008.
LCM(67004,67008) = 1122451008
Least Common Multiple of 67004 and 67008 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67004 and 67008, than apply into the LCM equation.
GCF(67004,67008) = 4
LCM(67004,67008) = ( 67004 × 67008) / 4
LCM(67004,67008) = 4489804032 / 4
LCM(67004,67008) = 1122451008
Least Common Multiple (LCM) of 67004 and 67008 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 67004 and 67008. First we will calculate the prime factors of 67004 and 67008.
Prime Factorization of 67004
Prime factors of 67004 are 2, 7, 2393. Prime factorization of 67004 in exponential form is:
67004 = 22 × 71 × 23931
Prime Factorization of 67008
Prime factors of 67008 are 2, 3, 349. Prime factorization of 67008 in exponential form is:
67008 = 26 × 31 × 3491
Now multiplying the highest exponent prime factors to calculate the LCM of 67004 and 67008.
LCM(67004,67008) = 26 × 71 × 23931 × 31 × 3491
LCM(67004,67008) = 1122451008
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