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What is the Least Common Multiple of 7290 and 7296?

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 7290 and 7296 is 8864640.

LCM(7290,7296) = 8864640

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Least Common Multiple of 7290 and 7296 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7290 and 7296, than apply into the LCM equation.

GCF(7290,7296) = 6
LCM(7290,7296) = ( 7290 × 7296) / 6
LCM(7290,7296) = 53187840 / 6
LCM(7290,7296) = 8864640

Least Common Multiple (LCM) of 7290 and 7296 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7290 and 7296. First we will calculate the prime factors of 7290 and 7296.

Prime Factorization of 7290

Prime factors of 7290 are 2, 3, 5. Prime factorization of 7290 in exponential form is:

7290 = 21 × 36 × 51

Prime Factorization of 7296

Prime factors of 7296 are 2, 3, 19. Prime factorization of 7296 in exponential form is:

7296 = 27 × 31 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 7290 and 7296.

LCM(7290,7296) = 27 × 36 × 51 × 191
LCM(7290,7296) = 8864640