Least Common Multiple (LCM) of 117 and 131
The least common multiple (LCM) of 117 and 131 is 15327.
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 117 and 131?
First, calculate the GCD of 117 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 131 = 0 remainder 117 |
| 2 | 131 ÷ 117 = 1 remainder 14 |
| 3 | 117 ÷ 14 = 8 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 193 | 2123 |
| 100 and 142 | 7100 |
| 36 and 141 | 1692 |
| 195 and 194 | 37830 |
| 126 and 39 | 1638 |