What is the Least Common Multiple of 31004 and 31008?
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 31004 and 31008 is 240343008.
LCM(31004,31008) = 240343008
Least Common Multiple of 31004 and 31008 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31004 and 31008, than apply into the LCM equation.
GCF(31004,31008) = 4
LCM(31004,31008) = ( 31004 × 31008) / 4
LCM(31004,31008) = 961372032 / 4
LCM(31004,31008) = 240343008
Least Common Multiple (LCM) of 31004 and 31008 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 31004 and 31008. First we will calculate the prime factors of 31004 and 31008.
Prime Factorization of 31004
Prime factors of 31004 are 2, 23, 337. Prime factorization of 31004 in exponential form is:
31004 = 22 × 231 × 3371
Prime Factorization of 31008
Prime factors of 31008 are 2, 3, 17, 19. Prime factorization of 31008 in exponential form is:
31008 = 25 × 31 × 171 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 31004 and 31008.
LCM(31004,31008) = 25 × 231 × 3371 × 31 × 171 × 191
LCM(31004,31008) = 240343008
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