Least Common Multiple (LCM) of 133 and 115
The least common multiple (LCM) of 133 and 115 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 133 and 115?
First, calculate the GCD of 133 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 115 = 1 remainder 18 |
| 2 | 115 ÷ 18 = 6 remainder 7 |
| 3 | 18 ÷ 7 = 2 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 187 | 187 |
| 59 and 109 | 6431 |
| 129 and 122 | 15738 |
| 171 and 68 | 11628 |
| 187 and 107 | 20009 |