Least Common Multiple (LCM) of 68 and 197
The least common multiple (LCM) of 68 and 197 is 13396.
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 68 and 197?
First, calculate the GCD of 68 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 197 = 0 remainder 68 |
| 2 | 197 ÷ 68 = 2 remainder 61 |
| 3 | 68 ÷ 61 = 1 remainder 7 |
| 4 | 61 ÷ 7 = 8 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 83 | 16268 |
| 67 and 123 | 8241 |
| 90 and 111 | 3330 |
| 137 and 125 | 17125 |
| 195 and 168 | 10920 |