Least Common Multiple (LCM) of 115 and 196
The least common multiple (LCM) of 115 and 196 is 22540.
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 115 and 196?
First, calculate the GCD of 115 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 196 = 0 remainder 115 |
| 2 | 196 ÷ 115 = 1 remainder 81 |
| 3 | 115 ÷ 81 = 1 remainder 34 |
| 4 | 81 ÷ 34 = 2 remainder 13 |
| 5 | 34 ÷ 13 = 2 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 32 | 160 |
| 80 and 200 | 400 |
| 34 and 135 | 4590 |
| 53 and 89 | 4717 |
| 37 and 147 | 5439 |