Least Common Multiple (LCM) of 128 and 100
The least common multiple (LCM) of 128 and 100 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 100?
First, calculate the GCD of 128 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 100 = 1 remainder 28 |
| 2 | 100 ÷ 28 = 3 remainder 16 |
| 3 | 28 ÷ 16 = 1 remainder 12 |
| 4 | 16 ÷ 12 = 1 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 68 | 3264 |
| 41 and 83 | 3403 |
| 106 and 55 | 5830 |
| 130 and 174 | 11310 |
| 130 and 193 | 25090 |