What is the Least Common Multiple of 572 and 585?
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 572 and 585 is 25740.
LCM(572,585) = 25740
Least Common Multiple of 572 and 585 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 572 and 585, than apply into the LCM equation.
GCF(572,585) = 13
LCM(572,585) = ( 572 × 585) / 13
LCM(572,585) = 334620 / 13
LCM(572,585) = 25740
Least Common Multiple (LCM) of 572 and 585 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 572 and 585. First we will calculate the prime factors of 572 and 585.
Prime Factorization of 572
Prime factors of 572 are 2, 11, 13. Prime factorization of 572 in exponential form is:
572 = 22 × 111 × 131
Prime Factorization of 585
Prime factors of 585 are 3, 5, 13. Prime factorization of 585 in exponential form is:
585 = 32 × 51 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 572 and 585.
LCM(572,585) = 22 × 111 × 131 × 32 × 51
LCM(572,585) = 25740
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