Least Common Multiple (LCM) of 197 and 67
The least common multiple (LCM) of 197 and 67 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 197 and 67?
First, calculate the GCD of 197 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 67 = 2 remainder 63 |
| 2 | 67 ÷ 63 = 1 remainder 4 |
| 3 | 63 ÷ 4 = 15 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 142 | 3834 |
| 69 and 45 | 1035 |
| 34 and 36 | 612 |
| 15 and 50 | 150 |
| 35 and 200 | 1400 |