Least Common Multiple (LCM) of 128 and 145
The least common multiple (LCM) of 128 and 145 is 18560.
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 145?
First, calculate the GCD of 128 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 145 = 0 remainder 128 |
| 2 | 145 ÷ 128 = 1 remainder 17 |
| 3 | 128 ÷ 17 = 7 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 53 | 2597 |
| 72 and 153 | 1224 |
| 11 and 55 | 55 |
| 135 and 170 | 4590 |
| 84 and 40 | 840 |