Least Common Multiple (LCM) of 115 and 133
The least common multiple (LCM) of 115 and 133 is 15295.
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 133?
First, calculate the GCD of 115 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 133 = 0 remainder 115 |
| 2 | 133 ÷ 115 = 1 remainder 18 |
| 3 | 115 ÷ 18 = 6 remainder 7 |
| 4 | 18 ÷ 7 = 2 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 63 | 3717 |
| 10 and 15 | 30 |
| 161 and 98 | 2254 |
| 72 and 82 | 2952 |
| 71 and 142 | 142 |