Least Common Multiple (LCM) of 165 and 128
The least common multiple (LCM) of 165 and 128 is 21120.
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 128?
First, calculate the GCD of 165 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 128 = 1 remainder 37 |
| 2 | 128 ÷ 37 = 3 remainder 17 |
| 3 | 37 ÷ 17 = 2 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 136 | 11016 |
| 94 and 165 | 15510 |
| 188 and 75 | 14100 |
| 198 and 56 | 5544 |
| 136 and 67 | 9112 |