Least Common Multiple (LCM) of 131 and 114
The least common multiple (LCM) of 131 and 114 is 14934.
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 131 and 114?
First, calculate the GCD of 131 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 114 = 1 remainder 17 |
| 2 | 114 ÷ 17 = 6 remainder 12 |
| 3 | 17 ÷ 12 = 1 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 200 | 11400 |
| 153 and 133 | 20349 |
| 194 and 96 | 9312 |
| 132 and 10 | 660 |
| 115 and 19 | 2185 |