Least Common Multiple (LCM) of 128 and 133
The least common multiple (LCM) of 128 and 133 is 17024.
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 133?
First, calculate the GCD of 128 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 133 = 0 remainder 128 |
| 2 | 133 ÷ 128 = 1 remainder 5 |
| 3 | 128 ÷ 5 = 25 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 64 | 2496 |
| 16 and 49 | 784 |
| 198 and 165 | 990 |
| 40 and 138 | 2760 |
| 119 and 165 | 19635 |