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What is the Least Common Multiple of 54696 and 54700?

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 54696 and 54700 is 747967800.

LCM(54696,54700) = 747967800

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Least Common Multiple of 54696 and 54700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54696 and 54700, than apply into the LCM equation.

GCF(54696,54700) = 4
LCM(54696,54700) = ( 54696 × 54700) / 4
LCM(54696,54700) = 2991871200 / 4
LCM(54696,54700) = 747967800

Least Common Multiple (LCM) of 54696 and 54700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54696 and 54700. First we will calculate the prime factors of 54696 and 54700.

Prime Factorization of 54696

Prime factors of 54696 are 2, 3, 43, 53. Prime factorization of 54696 in exponential form is:

54696 = 23 × 31 × 431 × 531

Prime Factorization of 54700

Prime factors of 54700 are 2, 5, 547. Prime factorization of 54700 in exponential form is:

54700 = 22 × 52 × 5471

Now multiplying the highest exponent prime factors to calculate the LCM of 54696 and 54700.

LCM(54696,54700) = 23 × 31 × 431 × 531 × 52 × 5471
LCM(54696,54700) = 747967800