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What is the Least Common Multiple of 25896 and 25900?

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 25896 and 25900 is 167676600.

LCM(25896,25900) = 167676600

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Least Common Multiple of 25896 and 25900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25896 and 25900, than apply into the LCM equation.

GCF(25896,25900) = 4
LCM(25896,25900) = ( 25896 × 25900) / 4
LCM(25896,25900) = 670706400 / 4
LCM(25896,25900) = 167676600

Least Common Multiple (LCM) of 25896 and 25900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25896 and 25900. First we will calculate the prime factors of 25896 and 25900.

Prime Factorization of 25896

Prime factors of 25896 are 2, 3, 13, 83. Prime factorization of 25896 in exponential form is:

25896 = 23 × 31 × 131 × 831

Prime Factorization of 25900

Prime factors of 25900 are 2, 5, 7, 37. Prime factorization of 25900 in exponential form is:

25900 = 22 × 52 × 71 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 25896 and 25900.

LCM(25896,25900) = 23 × 31 × 131 × 831 × 52 × 71 × 371
LCM(25896,25900) = 167676600