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What is the Least Common Multiple of 25989 and 26000?

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 25989 and 26000 is 675714000.

LCM(25989,26000) = 675714000

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Least Common Multiple of 25989 and 26000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25989 and 26000, than apply into the LCM equation.

GCF(25989,26000) = 1
LCM(25989,26000) = ( 25989 × 26000) / 1
LCM(25989,26000) = 675714000 / 1
LCM(25989,26000) = 675714000

Least Common Multiple (LCM) of 25989 and 26000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25989 and 26000. First we will calculate the prime factors of 25989 and 26000.

Prime Factorization of 25989

Prime factors of 25989 are 3, 8663. Prime factorization of 25989 in exponential form is:

25989 = 31 × 86631

Prime Factorization of 26000

Prime factors of 26000 are 2, 5, 13. Prime factorization of 26000 in exponential form is:

26000 = 24 × 53 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 25989 and 26000.

LCM(25989,26000) = 31 × 86631 × 24 × 53 × 131
LCM(25989,26000) = 675714000