Least Common Multiple (LCM) of 113 and 122
The least common multiple (LCM) of 113 and 122 is 13786.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 122?
First, calculate the GCD of 113 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 122 = 0 remainder 113 |
| 2 | 122 ÷ 113 = 1 remainder 9 |
| 3 | 113 ÷ 9 = 12 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 21 | 1197 |
| 174 and 51 | 2958 |
| 17 and 61 | 1037 |
| 101 and 195 | 19695 |
| 26 and 200 | 2600 |