What is the Least Common Multiple of 576 and 588?
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 576 and 588 is 28224.
LCM(576,588) = 28224
Least Common Multiple of 576 and 588 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 576 and 588, than apply into the LCM equation.
GCF(576,588) = 12
LCM(576,588) = ( 576 × 588) / 12
LCM(576,588) = 338688 / 12
LCM(576,588) = 28224
Least Common Multiple (LCM) of 576 and 588 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 576 and 588. First we will calculate the prime factors of 576 and 588.
Prime Factorization of 576
Prime factors of 576 are 2, 3. Prime factorization of 576 in exponential form is:
576 = 26 × 32
Prime Factorization of 588
Prime factors of 588 are 2, 3, 7. Prime factorization of 588 in exponential form is:
588 = 22 × 31 × 72
Now multiplying the highest exponent prime factors to calculate the LCM of 576 and 588.
LCM(576,588) = 26 × 32 × 72
LCM(576,588) = 28224
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