What is the Least Common Multiple of 2600 and 2609?

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 2600 and 2609 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2600 and 2609, than apply into the LCM equation.

GCF(2600,2609) = 1
LCM(2600,2609) = ( 2600 × 2609) / 1
LCM(2600,2609) = 6783400 / 1
LCM(2600,2609) = 6783400

Least Common Multiple (LCM) of 2600 and 2609 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2600 and 2609. First we will calculate the prime factors of 2600 and 2609.

Prime Factorization of 2600

Prime Factorization of 2609

Now multiplying the highest exponent prime factors to calculate the LCM of 2600 and 2609.

LCM(2600,2609) = 2³ × 5² × 13¹ × 2609¹
LCM(2600,2609) = 6783400