Least Common Multiple (LCM) of 41 and 114
The least common multiple (LCM) of 41 and 114 is 4674.
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 114?
First, calculate the GCD of 41 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 114 = 0 remainder 41 |
| 2 | 114 ÷ 41 = 2 remainder 32 |
| 3 | 41 ÷ 32 = 1 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 81 | 3726 |
| 107 and 199 | 21293 |
| 146 and 18 | 1314 |
| 121 and 198 | 2178 |
| 175 and 76 | 13300 |