Least Common Multiple (LCM) of 128 and 165
The least common multiple (LCM) of 128 and 165 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 128 and 165?
First, calculate the GCD of 128 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 165 = 0 remainder 128 |
| 2 | 165 ÷ 128 = 1 remainder 37 |
| 3 | 128 ÷ 37 = 3 remainder 17 |
| 4 | 37 ÷ 17 = 2 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 192 | 192 |
| 12 and 37 | 444 |
| 131 and 72 | 9432 |
| 75 and 86 | 6450 |
| 80 and 157 | 12560 |