Least Common Multiple (LCM) of 199 and 140
The least common multiple (LCM) of 199 and 140 is 27860.
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 199 and 140?
First, calculate the GCD of 199 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 140 = 1 remainder 59 |
| 2 | 140 ÷ 59 = 2 remainder 22 |
| 3 | 59 ÷ 22 = 2 remainder 15 |
| 4 | 22 ÷ 15 = 1 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 32 | 800 |
| 49 and 165 | 8085 |
| 104 and 20 | 520 |
| 28 and 89 | 2492 |
| 87 and 118 | 10266 |