Least Common Multiple (LCM) of 196 and 67
The least common multiple (LCM) of 196 and 67 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 196 and 67?
First, calculate the GCD of 196 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 67 = 2 remainder 62 |
| 2 | 67 ÷ 62 = 1 remainder 5 |
| 3 | 62 ÷ 5 = 12 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 67 | 7638 |
| 194 and 168 | 16296 |
| 45 and 189 | 945 |
| 40 and 19 | 760 |
| 186 and 22 | 2046 |