Least Common Multiple (LCM) of 199 and 52
The least common multiple (LCM) of 199 and 52 is 10348.
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 52?
First, calculate the GCD of 199 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 52 = 3 remainder 43 |
| 2 | 52 ÷ 43 = 1 remainder 9 |
| 3 | 43 ÷ 9 = 4 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 103 | 8343 |
| 189 and 123 | 7749 |
| 28 and 198 | 2772 |
| 72 and 113 | 8136 |
| 114 and 11 | 1254 |