What is the Least Common Multiple of 564 and 570?
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 570 is 53580.
LCM(564,570) = 53580
Least Common Multiple of 564 and 570 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 570, than apply into the LCM equation.
GCF(564,570) = 6
LCM(564,570) = ( 564 × 570) / 6
LCM(564,570) = 321480 / 6
LCM(564,570) = 53580
Least Common Multiple (LCM) of 564 and 570 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 564 and 570. First we will calculate the prime factors of 564 and 570.
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 570
Prime factors of 570 are 2, 3, 5, 19. Prime factorization of 570 in exponential form is:
570 = 21 × 31 × 51 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 564 and 570.
LCM(564,570) = 22 × 31 × 471 × 51 × 191
LCM(564,570) = 53580
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Related Least Common Multiples of 570
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