Least Common Multiple (LCM) of 41 and 117
The least common multiple (LCM) of 41 and 117 is 4797.
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 117?
First, calculate the GCD of 41 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 117 = 0 remainder 41 |
| 2 | 117 ÷ 41 = 2 remainder 35 |
| 3 | 41 ÷ 35 = 1 remainder 6 |
| 4 | 35 ÷ 6 = 5 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 97 | 6208 |
| 20 and 26 | 260 |
| 129 and 67 | 8643 |
| 101 and 63 | 6363 |
| 123 and 145 | 17835 |