Least Common Multiple (LCM) of 199 and 56
The least common multiple (LCM) of 199 and 56 is 11144.
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 56?
First, calculate the GCD of 199 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 56 = 3 remainder 31 |
| 2 | 56 ÷ 31 = 1 remainder 25 |
| 3 | 31 ÷ 25 = 1 remainder 6 |
| 4 | 25 ÷ 6 = 4 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 74 | 5550 |
| 146 and 137 | 20002 |
| 200 and 116 | 5800 |
| 102 and 52 | 2652 |
| 59 and 194 | 11446 |