Least Common Multiple (LCM) of 131 and 165
The least common multiple (LCM) of 131 and 165 is 21615.
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 165?
First, calculate the GCD of 131 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 165 = 0 remainder 131 |
| 2 | 165 ÷ 131 = 1 remainder 34 |
| 3 | 131 ÷ 34 = 3 remainder 29 |
| 4 | 34 ÷ 29 = 1 remainder 5 |
| 5 | 29 ÷ 5 = 5 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 167 | 10688 |
| 31 and 92 | 2852 |
| 45 and 14 | 630 |
| 31 and 29 | 899 |
| 55 and 71 | 3905 |