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What is the Least Common Multiple of 54309 and 54315?

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 54309 and 54315 is 983264445.

LCM(54309,54315) = 983264445

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Least Common Multiple of 54309 and 54315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54309 and 54315, than apply into the LCM equation.

GCF(54309,54315) = 3
LCM(54309,54315) = ( 54309 × 54315) / 3
LCM(54309,54315) = 2949793335 / 3
LCM(54309,54315) = 983264445

Least Common Multiple (LCM) of 54309 and 54315 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54309 and 54315. First we will calculate the prime factors of 54309 and 54315.

Prime Factorization of 54309

Prime factors of 54309 are 3, 43, 421. Prime factorization of 54309 in exponential form is:

54309 = 31 × 431 × 4211

Prime Factorization of 54315

Prime factors of 54315 are 3, 5, 17, 71. Prime factorization of 54315 in exponential form is:

54315 = 32 × 51 × 171 × 711

Now multiplying the highest exponent prime factors to calculate the LCM of 54309 and 54315.

LCM(54309,54315) = 32 × 431 × 4211 × 51 × 171 × 711
LCM(54309,54315) = 983264445