What is the Least Common Multiple of 67002 and 67022?
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 67002 and 67022 is 2245304022.
LCM(67002,67022) = 2245304022
Least Common Multiple of 67002 and 67022 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67002 and 67022, than apply into the LCM equation.
GCF(67002,67022) = 2
LCM(67002,67022) = ( 67002 × 67022) / 2
LCM(67002,67022) = 4490608044 / 2
LCM(67002,67022) = 2245304022
Least Common Multiple (LCM) of 67002 and 67022 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 67002 and 67022. First we will calculate the prime factors of 67002 and 67022.
Prime Factorization of 67002
Prime factors of 67002 are 2, 3, 13, 859. Prime factorization of 67002 in exponential form is:
67002 = 21 × 31 × 131 × 8591
Prime Factorization of 67022
Prime factors of 67022 are 2, 23, 31, 47. Prime factorization of 67022 in exponential form is:
67022 = 21 × 231 × 311 × 471
Now multiplying the highest exponent prime factors to calculate the LCM of 67002 and 67022.
LCM(67002,67022) = 21 × 31 × 131 × 8591 × 231 × 311 × 471
LCM(67002,67022) = 2245304022
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