Least Common Multiple (LCM) of 41 and 189
The least common multiple (LCM) of 41 and 189 is 7749.
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 41 and 189?
First, calculate the GCD of 41 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 189 = 0 remainder 41 |
| 2 | 189 ÷ 41 = 4 remainder 25 |
| 3 | 41 ÷ 25 = 1 remainder 16 |
| 4 | 25 ÷ 16 = 1 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 52 | 4628 |
| 24 and 113 | 2712 |
| 31 and 188 | 5828 |
| 196 and 134 | 13132 |
| 197 and 133 | 26201 |