Least Common Multiple (LCM) of 113 and 161
The least common multiple (LCM) of 113 and 161 is 18193.
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 161?
First, calculate the GCD of 113 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 161 = 0 remainder 113 |
| 2 | 161 ÷ 113 = 1 remainder 48 |
| 3 | 113 ÷ 48 = 2 remainder 17 |
| 4 | 48 ÷ 17 = 2 remainder 14 |
| 5 | 17 ÷ 14 = 1 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 131 | 3275 |
| 194 and 73 | 14162 |
| 198 and 183 | 12078 |
| 144 and 26 | 1872 |
| 196 and 177 | 34692 |