Least Common Multiple (LCM) of 165 and 133
The least common multiple (LCM) of 165 and 133 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 165 and 133?
First, calculate the GCD of 165 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 133 = 1 remainder 32 |
| 2 | 133 ÷ 32 = 4 remainder 5 |
| 3 | 32 ÷ 5 = 6 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 158 | 7426 |
| 147 and 107 | 15729 |
| 179 and 44 | 7876 |
| 105 and 128 | 13440 |
| 189 and 75 | 4725 |