Least Common Multiple (LCM) of 40 and 197
The least common multiple (LCM) of 40 and 197 is 7880.
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 40 and 197?
First, calculate the GCD of 40 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 197 = 0 remainder 40 |
| 2 | 197 ÷ 40 = 4 remainder 37 |
| 3 | 40 ÷ 37 = 1 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 83 | 8881 |
| 106 and 18 | 954 |
| 129 and 41 | 5289 |
| 58 and 168 | 4872 |
| 138 and 188 | 12972 |