Least Common Multiple (LCM) of 133 and 165
The least common multiple (LCM) of 133 and 165 is 21945.
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 133 and 165?
First, calculate the GCD of 133 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 165 = 0 remainder 133 |
| 2 | 165 ÷ 133 = 1 remainder 32 |
| 3 | 133 ÷ 32 = 4 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 198 | 1980 |
| 20 and 21 | 420 |
| 194 and 62 | 6014 |
| 39 and 178 | 6942 |
| 123 and 191 | 23493 |