Least Common Multiple (LCM) of 128 and 196
The least common multiple (LCM) of 128 and 196 is 6272.
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 196?
First, calculate the GCD of 128 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 196 = 0 remainder 128 |
| 2 | 196 ÷ 128 = 1 remainder 68 |
| 3 | 128 ÷ 68 = 1 remainder 60 |
| 4 | 68 ÷ 60 = 1 remainder 8 |
| 5 | 60 ÷ 8 = 7 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 80 | 240 |
| 69 and 41 | 2829 |
| 136 and 139 | 18904 |
| 78 and 38 | 1482 |
| 77 and 77 | 77 |