Least Common Multiple (LCM) of 131 and 177
The least common multiple (LCM) of 131 and 177 is 23187.
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 177?
First, calculate the GCD of 131 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 177 = 0 remainder 131 |
| 2 | 177 ÷ 131 = 1 remainder 46 |
| 3 | 131 ÷ 46 = 2 remainder 39 |
| 4 | 46 ÷ 39 = 1 remainder 7 |
| 5 | 39 ÷ 7 = 5 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 30 | 510 |
| 30 and 30 | 30 |
| 84 and 60 | 420 |
| 39 and 144 | 1872 |
| 78 and 109 | 8502 |