Least Common Multiple (LCM) of 197 and 68
The least common multiple (LCM) of 197 and 68 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 197 and 68?
First, calculate the GCD of 197 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 68 = 2 remainder 61 |
| 2 | 68 ÷ 61 = 1 remainder 7 |
| 3 | 61 ÷ 7 = 8 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 161 | 31234 |
| 75 and 33 | 825 |
| 165 and 79 | 13035 |
| 170 and 89 | 15130 |
| 143 and 17 | 2431 |