What is the Least Common Multiple of 578 and 596?
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 578 and 596 is 172244.
LCM(578,596) = 172244
Least Common Multiple of 578 and 596 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 578 and 596, than apply into the LCM equation.
GCF(578,596) = 2
LCM(578,596) = ( 578 × 596) / 2
LCM(578,596) = 344488 / 2
LCM(578,596) = 172244
Least Common Multiple (LCM) of 578 and 596 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 578 and 596. First we will calculate the prime factors of 578 and 596.
Prime Factorization of 578
Prime factors of 578 are 2, 17. Prime factorization of 578 in exponential form is:
578 = 21 × 172
Prime Factorization of 596
Prime factors of 596 are 2, 149. Prime factorization of 596 in exponential form is:
596 = 22 × 1491
Now multiplying the highest exponent prime factors to calculate the LCM of 578 and 596.
LCM(578,596) = 22 × 172 × 1491
LCM(578,596) = 172244
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