Least Common Multiple (LCM) of 67 and 197
The least common multiple (LCM) of 67 and 197 is 13199.
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 197?
First, calculate the GCD of 67 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 197 = 0 remainder 67 |
| 2 | 197 ÷ 67 = 2 remainder 63 |
| 3 | 67 ÷ 63 = 1 remainder 4 |
| 4 | 63 ÷ 4 = 15 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 177 | 11859 |
| 60 and 127 | 7620 |
| 59 and 191 | 11269 |
| 174 and 108 | 3132 |
| 114 and 67 | 7638 |