Least Common Multiple (LCM) of 199 and 143
The least common multiple (LCM) of 199 and 143 is 28457.
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 143?
First, calculate the GCD of 199 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 143 = 1 remainder 56 |
| 2 | 143 ÷ 56 = 2 remainder 31 |
| 3 | 56 ÷ 31 = 1 remainder 25 |
| 4 | 31 ÷ 25 = 1 remainder 6 |
| 5 | 25 ÷ 6 = 4 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 164 | 17876 |
| 79 and 17 | 1343 |
| 164 and 169 | 27716 |
| 89 and 63 | 5607 |
| 105 and 80 | 1680 |