Least Common Multiple (LCM) of 196 and 115
The least common multiple (LCM) of 196 and 115 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 196 and 115?
First, calculate the GCD of 196 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 115 = 1 remainder 81 |
| 2 | 115 ÷ 81 = 1 remainder 34 |
| 3 | 81 ÷ 34 = 2 remainder 13 |
| 4 | 34 ÷ 13 = 2 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 82 | 410 |
| 101 and 11 | 1111 |
| 116 and 113 | 13108 |
| 154 and 58 | 4466 |
| 54 and 124 | 3348 |