What is the Least Common Multiple of 25980 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 of 25980 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 25980 and 26000, than apply into the LCM equation.

GCF(25980,26000) = 20
LCM(25980,26000) = ( 25980 × 26000) / 20
LCM(25980,26000) = 675480000 / 20
LCM(25980,26000) = 33774000

Least Common Multiple (LCM) of 25980 and 26000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25980 and 26000. First we will calculate the prime factors of 25980 and 26000.

Prime Factorization of 25980

Prime Factorization of 26000

Now multiplying the highest exponent prime factors to calculate the LCM of 25980 and 26000.

LCM(25980,26000) = 2⁴ × 3¹ × 5³ × 433¹ × 13¹
LCM(25980,26000) = 33774000