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What is the Least Common Multiple of 25860 and 25872?

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 25860 and 25872 is 55754160.

LCM(25860,25872) = 55754160

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Least Common Multiple of 25860 and 25872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25860 and 25872, than apply into the LCM equation.

GCF(25860,25872) = 12
LCM(25860,25872) = ( 25860 × 25872) / 12
LCM(25860,25872) = 669049920 / 12
LCM(25860,25872) = 55754160

Least Common Multiple (LCM) of 25860 and 25872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25860 and 25872. First we will calculate the prime factors of 25860 and 25872.

Prime Factorization of 25860

Prime factors of 25860 are 2, 3, 5, 431. Prime factorization of 25860 in exponential form is:

25860 = 22 × 31 × 51 × 4311

Prime Factorization of 25872

Prime factors of 25872 are 2, 3, 7, 11. Prime factorization of 25872 in exponential form is:

25872 = 24 × 31 × 72 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 25860 and 25872.

LCM(25860,25872) = 24 × 31 × 51 × 4311 × 72 × 111
LCM(25860,25872) = 55754160