Least Common Multiple (LCM) of 116 and 131
The least common multiple (LCM) of 116 and 131 is 15196.
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 116 and 131?
First, calculate the GCD of 116 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 131 = 0 remainder 116 |
| 2 | 131 ÷ 116 = 1 remainder 15 |
| 3 | 116 ÷ 15 = 7 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 49 | 294 |
| 27 and 186 | 1674 |
| 96 and 72 | 288 |
| 92 and 155 | 14260 |
| 138 and 108 | 2484 |