What is the Least Common Multiple of 570 and 589?
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 570 and 589 is 17670.
LCM(570,589) = 17670
Least Common Multiple of 570 and 589 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 570 and 589, than apply into the LCM equation.
GCF(570,589) = 19
LCM(570,589) = ( 570 × 589) / 19
LCM(570,589) = 335730 / 19
LCM(570,589) = 17670
Least Common Multiple (LCM) of 570 and 589 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 570 and 589. First we will calculate the prime factors of 570 and 589.
Prime Factorization of 570
Prime factors of 570 are 2, 3, 5, 19. Prime factorization of 570 in exponential form is:
570 = 21 × 31 × 51 × 191
Prime Factorization of 589
Prime factors of 589 are 19, 31. Prime factorization of 589 in exponential form is:
589 = 191 × 311
Now multiplying the highest exponent prime factors to calculate the LCM of 570 and 589.
LCM(570,589) = 21 × 31 × 51 × 191 × 311
LCM(570,589) = 17670
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