Least Common Multiple (LCM) of 67 and 196
The least common multiple (LCM) of 67 and 196 is 13132.
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 67 and 196?
First, calculate the GCD of 67 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 196 = 0 remainder 67 |
| 2 | 196 ÷ 67 = 2 remainder 62 |
| 3 | 67 ÷ 62 = 1 remainder 5 |
| 4 | 62 ÷ 5 = 12 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 158 | 23226 |
| 85 and 13 | 1105 |
| 177 and 24 | 1416 |
| 187 and 132 | 2244 |
| 29 and 59 | 1711 |