Least Common Multiple (LCM) of 106 and 41
The least common multiple (LCM) of 106 and 41 is 4346.
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 106 and 41?
First, calculate the GCD of 106 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 41 = 2 remainder 24 |
| 2 | 41 ÷ 24 = 1 remainder 17 |
| 3 | 24 ÷ 17 = 1 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 127 | 16256 |
| 100 and 181 | 18100 |
| 171 and 84 | 4788 |
| 160 and 34 | 2720 |
| 51 and 50 | 2550 |