Least Common Multiple (LCM) of 196 and 128
The least common multiple (LCM) of 196 and 128 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 196 and 128?
First, calculate the GCD of 196 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 128 = 1 remainder 68 |
| 2 | 128 ÷ 68 = 1 remainder 60 |
| 3 | 68 ÷ 60 = 1 remainder 8 |
| 4 | 60 ÷ 8 = 7 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 35 | 2380 |
| 138 and 177 | 8142 |
| 44 and 18 | 396 |
| 61 and 58 | 3538 |
| 35 and 45 | 315 |