Least Common Multiple (LCM) of 128 and 200
The least common multiple (LCM) of 128 and 200 is 3200.
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 200?
First, calculate the GCD of 128 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 200 = 0 remainder 128 |
| 2 | 200 ÷ 128 = 1 remainder 72 |
| 3 | 128 ÷ 72 = 1 remainder 56 |
| 4 | 72 ÷ 56 = 1 remainder 16 |
| 5 | 56 ÷ 16 = 3 remainder 8 |
| 6 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 17 | 425 |
| 100 and 36 | 900 |
| 182 and 181 | 32942 |
| 65 and 13 | 65 |
| 159 and 104 | 16536 |