Least Common Multiple (LCM) of 128 and 171
The least common multiple (LCM) of 128 and 171 is 21888.
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 171?
First, calculate the GCD of 128 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 171 = 0 remainder 128 |
| 2 | 171 ÷ 128 = 1 remainder 43 |
| 3 | 128 ÷ 43 = 2 remainder 42 |
| 4 | 43 ÷ 42 = 1 remainder 1 |
| 5 | 42 ÷ 1 = 42 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 109 | 1962 |
| 68 and 44 | 748 |
| 141 and 25 | 3525 |
| 23 and 40 | 920 |
| 112 and 97 | 10864 |