What is the Least Common Multiple of 30586 and 30590?
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 30586 and 30590 is 467812870.
LCM(30586,30590) = 467812870
Least Common Multiple of 30586 and 30590 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30586 and 30590, than apply into the LCM equation.
GCF(30586,30590) = 2
LCM(30586,30590) = ( 30586 × 30590) / 2
LCM(30586,30590) = 935625740 / 2
LCM(30586,30590) = 467812870
Least Common Multiple (LCM) of 30586 and 30590 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 30586 and 30590. First we will calculate the prime factors of 30586 and 30590.
Prime Factorization of 30586
Prime factors of 30586 are 2, 41, 373. Prime factorization of 30586 in exponential form is:
30586 = 21 × 411 × 3731
Prime Factorization of 30590
Prime factors of 30590 are 2, 5, 7, 19, 23. Prime factorization of 30590 in exponential form is:
30590 = 21 × 51 × 71 × 191 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 30586 and 30590.
LCM(30586,30590) = 21 × 411 × 3731 × 51 × 71 × 191 × 231
LCM(30586,30590) = 467812870
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