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What is the Least Common Multiple of 7284 and 7300?

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 7284 and 7300 is 13293300.

LCM(7284,7300) = 13293300

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Least Common Multiple of 7284 and 7300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7284 and 7300, than apply into the LCM equation.

GCF(7284,7300) = 4
LCM(7284,7300) = ( 7284 × 7300) / 4
LCM(7284,7300) = 53173200 / 4
LCM(7284,7300) = 13293300

Least Common Multiple (LCM) of 7284 and 7300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7284 and 7300. First we will calculate the prime factors of 7284 and 7300.

Prime Factorization of 7284

Prime factors of 7284 are 2, 3, 607. Prime factorization of 7284 in exponential form is:

7284 = 22 × 31 × 6071

Prime Factorization of 7300

Prime factors of 7300 are 2, 5, 73. Prime factorization of 7300 in exponential form is:

7300 = 22 × 52 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 7284 and 7300.

LCM(7284,7300) = 22 × 31 × 6071 × 52 × 731
LCM(7284,7300) = 13293300