Least Common Multiple (LCM) of 128 and 194
The least common multiple (LCM) of 128 and 194 is 12416.
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 194?
First, calculate the GCD of 128 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 194 = 0 remainder 128 |
| 2 | 194 ÷ 128 = 1 remainder 66 |
| 3 | 128 ÷ 66 = 1 remainder 62 |
| 4 | 66 ÷ 62 = 1 remainder 4 |
| 5 | 62 ÷ 4 = 15 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 15 | 660 |
| 72 and 19 | 1368 |
| 190 and 68 | 6460 |
| 160 and 49 | 7840 |
| 31 and 116 | 3596 |