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What is the Least Common Multiple of 7584 and 7588?

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 7584 and 7588 is 14386848.

LCM(7584,7588) = 14386848

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Least Common Multiple of 7584 and 7588 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7584 and 7588, than apply into the LCM equation.

GCF(7584,7588) = 4
LCM(7584,7588) = ( 7584 × 7588) / 4
LCM(7584,7588) = 57547392 / 4
LCM(7584,7588) = 14386848

Least Common Multiple (LCM) of 7584 and 7588 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7584 and 7588. First we will calculate the prime factors of 7584 and 7588.

Prime Factorization of 7584

Prime factors of 7584 are 2, 3, 79. Prime factorization of 7584 in exponential form is:

7584 = 25 × 31 × 791

Prime Factorization of 7588

Prime factors of 7588 are 2, 7, 271. Prime factorization of 7588 in exponential form is:

7588 = 22 × 71 × 2711

Now multiplying the highest exponent prime factors to calculate the LCM of 7584 and 7588.

LCM(7584,7588) = 25 × 31 × 791 × 71 × 2711
LCM(7584,7588) = 14386848