Least Common Multiple (LCM) of 165 and 131
The least common multiple (LCM) of 165 and 131 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 165 and 131?
First, calculate the GCD of 165 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 131 = 1 remainder 34 |
| 2 | 131 ÷ 34 = 3 remainder 29 |
| 3 | 34 ÷ 29 = 1 remainder 5 |
| 4 | 29 ÷ 5 = 5 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 12 | 1644 |
| 29 and 106 | 3074 |
| 111 and 138 | 5106 |
| 102 and 55 | 5610 |
| 41 and 149 | 6109 |