Least Common Multiple (LCM) of 29 and 199
The least common multiple (LCM) of 29 and 199 is 5771.
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 29 and 199?
First, calculate the GCD of 29 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 199 = 0 remainder 29 |
| 2 | 199 ÷ 29 = 6 remainder 25 |
| 3 | 29 ÷ 25 = 1 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 71 | 8023 |
| 136 and 11 | 1496 |
| 153 and 75 | 3825 |
| 98 and 116 | 5684 |
| 180 and 15 | 180 |