Least Common Multiple (LCM) of 105 and 41
The least common multiple (LCM) of 105 and 41 is 4305.
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 105 and 41?
First, calculate the GCD of 105 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 41 = 2 remainder 23 |
| 2 | 41 ÷ 23 = 1 remainder 18 |
| 3 | 23 ÷ 18 = 1 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 53 | 1166 |
| 10 and 64 | 320 |
| 102 and 170 | 510 |
| 159 and 175 | 27825 |
| 176 and 82 | 7216 |