GCF(205, 11) = 1 | LCM = 2,255
GCF of 205 and 11 is 1. LCM is 2,255. Free GCF LCM calculator with prime factorization.
GCF x LCM = 205 x 11 = 2,255. GCF = 1, LCM = 2,255/1 = 2,255.
How This Was Calculated
GCF (Greatest Common Factor) is found with the Euclidean algorithm: repeatedly replace the larger number by the remainder of dividing the two, until the remainder is zero.
LCM (Least Common Multiple) uses the relationship: LCM(a, b) = (a x b) / GCF(a, b)
For any two positive integers, GCF x LCM always equals the product of the two numbers.
Frequently Asked Questions
What is the GCF?
The Greatest Common Factor (also called GCD or HCF) is the largest number that divides both numbers exactly. For 12 and 18, the GCF is 6.
What is the LCM?
The Least Common Multiple is the smallest number that both numbers divide into exactly. For 12 and 18, the LCM is 36.
When do I use GCF vs LCM?
Use GCF when splitting things into equal groups or simplifying fractions. Use LCM when finding common denominators or scheduling repeating events.
What if the GCF is 1?
The numbers are called coprime (relatively prime) — they share no common factors. Their LCM is simply their product. Example: 7 and 13.
Does GCF x LCM always equal a x b?
Yes, for any two positive integers: GCF(a,b) x LCM(a,b) = a x b. This identity lets you find one from the other.