Least Common Multiple (LCM) of 165 and 191
The least common multiple (LCM) of 165 and 191 is 31515.
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 191?
First, calculate the GCD of 165 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 191 = 0 remainder 165 |
| 2 | 191 ÷ 165 = 1 remainder 26 |
| 3 | 165 ÷ 26 = 6 remainder 9 |
| 4 | 26 ÷ 9 = 2 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 126 | 882 |
| 36 and 54 | 108 |
| 200 and 11 | 2200 |
| 122 and 37 | 4514 |
| 198 and 53 | 10494 |