Least Common Multiple (LCM) of 22 and 128
The least common multiple (LCM) of 22 and 128 is 1408.
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 22 and 128?
First, calculate the GCD of 22 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 128 = 0 remainder 22 |
| 2 | 128 ÷ 22 = 5 remainder 18 |
| 3 | 22 ÷ 18 = 1 remainder 4 |
| 4 | 18 ÷ 4 = 4 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 45 | 2385 |
| 42 and 128 | 2688 |
| 38 and 147 | 5586 |
| 55 and 172 | 9460 |
| 73 and 145 | 10585 |