Least Common Multiple (LCM) of 113 and 196
The least common multiple (LCM) of 113 and 196 is 22148.
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 196?
First, calculate the GCD of 113 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 196 = 0 remainder 113 |
| 2 | 196 ÷ 113 = 1 remainder 83 |
| 3 | 113 ÷ 83 = 1 remainder 30 |
| 4 | 83 ÷ 30 = 2 remainder 23 |
| 5 | 30 ÷ 23 = 1 remainder 7 |
| 6 | 23 ÷ 7 = 3 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 199 | 33631 |
| 51 and 147 | 2499 |
| 161 and 189 | 4347 |
| 187 and 51 | 561 |
| 178 and 97 | 17266 |