Least Common Multiple (LCM) of 140 and 198
The least common multiple (LCM) of 140 and 198 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 140 and 198?
First, calculate the GCD of 140 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 198 = 0 remainder 140 |
| 2 | 198 ÷ 140 = 1 remainder 58 |
| 3 | 140 ÷ 58 = 2 remainder 24 |
| 4 | 58 ÷ 24 = 2 remainder 10 |
| 5 | 24 ÷ 10 = 2 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 67 | 2613 |
| 175 and 107 | 18725 |
| 169 and 74 | 12506 |
| 134 and 173 | 23182 |
| 45 and 51 | 765 |