Least Common Multiple (LCM) of 41 and 54
The least common multiple (LCM) of 41 and 54 is 2214.
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 54?
First, calculate the GCD of 41 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 54 = 0 remainder 41 |
| 2 | 54 ÷ 41 = 1 remainder 13 |
| 3 | 41 ÷ 13 = 3 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 31 | 4154 |
| 131 and 162 | 21222 |
| 107 and 133 | 14231 |
| 45 and 108 | 540 |
| 180 and 114 | 3420 |