Least Common Multiple (LCM) of 198 and 140
The least common multiple (LCM) of 198 and 140 is 13860.
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 198 and 140?
First, calculate the GCD of 198 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 140 = 1 remainder 58 |
| 2 | 140 ÷ 58 = 2 remainder 24 |
| 3 | 58 ÷ 24 = 2 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 17 | 1785 |
| 147 and 19 | 2793 |
| 104 and 190 | 9880 |
| 107 and 74 | 7918 |
| 144 and 22 | 1584 |