Least Common Multiple (LCM) of 168 and 197
The least common multiple (LCM) of 168 and 197 is 33096.
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 168 and 197?
First, calculate the GCD of 168 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 197 = 0 remainder 168 |
| 2 | 197 ÷ 168 = 1 remainder 29 |
| 3 | 168 ÷ 29 = 5 remainder 23 |
| 4 | 29 ÷ 23 = 1 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 73 | 2701 |
| 159 and 144 | 7632 |
| 74 and 37 | 74 |
| 125 and 83 | 10375 |
| 123 and 198 | 8118 |