What is the Least Common Multiple of 564 and 582?
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 564 and 582 is 54708.
LCM(564,582) = 54708
Least Common Multiple of 564 and 582 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 564 and 582, than apply into the LCM equation.
GCF(564,582) = 6
LCM(564,582) = ( 564 × 582) / 6
LCM(564,582) = 328248 / 6
LCM(564,582) = 54708
Least Common Multiple (LCM) of 564 and 582 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 564 and 582. First we will calculate the prime factors of 564 and 582.
Prime Factorization of 564
Prime factors of 564 are 2, 3, 47. Prime factorization of 564 in exponential form is:
564 = 22 × 31 × 471
Prime Factorization of 582
Prime factors of 582 are 2, 3, 97. Prime factorization of 582 in exponential form is:
582 = 21 × 31 × 971
Now multiplying the highest exponent prime factors to calculate the LCM of 564 and 582.
LCM(564,582) = 22 × 31 × 471 × 971
LCM(564,582) = 54708
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