Least Common Multiple (LCM) of 41 and 138
The least common multiple (LCM) of 41 and 138 is 5658.
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 138?
First, calculate the GCD of 41 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 138 = 0 remainder 41 |
| 2 | 138 ÷ 41 = 3 remainder 15 |
| 3 | 41 ÷ 15 = 2 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 46 | 4830 |
| 59 and 103 | 6077 |
| 73 and 110 | 8030 |
| 75 and 153 | 3825 |
| 137 and 77 | 10549 |