What is the Least Common Multiple of 584 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 584 and 590 is 172280.
LCM(584,590) = 172280
Least Common Multiple of 584 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 584 and 590, than apply into the LCM equation.
GCF(584,590) = 2
LCM(584,590) = ( 584 × 590) / 2
LCM(584,590) = 344560 / 2
LCM(584,590) = 172280
Least Common Multiple (LCM) of 584 and 590 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 584 and 590. First we will calculate the prime factors of 584 and 590.
Prime Factorization of 584
Prime factors of 584 are 2, 73. Prime factorization of 584 in exponential form is:
584 = 23 × 731
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 584 and 590.
LCM(584,590) = 23 × 731 × 51 × 591
LCM(584,590) = 172280
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