What is the Least Common Multiple of 570 and 590?
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 590 is 33630.
LCM(570,590) = 33630
Least Common Multiple of 570 and 590 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 590, than apply into the LCM equation.
GCF(570,590) = 10
LCM(570,590) = ( 570 × 590) / 10
LCM(570,590) = 336300 / 10
LCM(570,590) = 33630
Least Common Multiple (LCM) of 570 and 590 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 570 and 590. First we will calculate the prime factors of 570 and 590.
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 590
Prime factors of 590 are 2, 5, 59. Prime factorization of 590 in exponential form is:
590 = 21 × 51 × 591
Now multiplying the highest exponent prime factors to calculate the LCM of 570 and 590.
LCM(570,590) = 21 × 31 × 51 × 191 × 591
LCM(570,590) = 33630
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