Least Common Multiple (LCM) of 143 and 199
The least common multiple (LCM) of 143 and 199 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 143 and 199?
First, calculate the GCD of 143 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 199 = 0 remainder 143 |
| 2 | 199 ÷ 143 = 1 remainder 56 |
| 3 | 143 ÷ 56 = 2 remainder 31 |
| 4 | 56 ÷ 31 = 1 remainder 25 |
| 5 | 31 ÷ 25 = 1 remainder 6 |
| 6 | 25 ÷ 6 = 4 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 179 | 17721 |
| 177 and 194 | 34338 |
| 188 and 38 | 3572 |
| 172 and 46 | 3956 |
| 114 and 57 | 114 |