Least Common Multiple (LCM) of 41 and 105
The least common multiple (LCM) of 41 and 105 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 41 and 105?
First, calculate the GCD of 41 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 105 = 0 remainder 41 |
| 2 | 105 ÷ 41 = 2 remainder 23 |
| 3 | 41 ÷ 23 = 1 remainder 18 |
| 4 | 23 ÷ 18 = 1 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 111 | 19536 |
| 190 and 128 | 12160 |
| 115 and 72 | 8280 |
| 17 and 152 | 2584 |
| 123 and 27 | 1107 |