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 |
|---|---|
| 152 and 113 | 17176 |
| 166 and 99 | 16434 |
| 200 and 43 | 8600 |
| 165 and 104 | 17160 |
| 121 and 84 | 10164 |