Least Common Multiple (LCM) of 41 and 177
The least common multiple (LCM) of 41 and 177 is 7257.
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 177?
First, calculate the GCD of 41 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 177 = 0 remainder 41 |
| 2 | 177 ÷ 41 = 4 remainder 13 |
| 3 | 41 ÷ 13 = 3 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 11 | 1485 |
| 57 and 88 | 5016 |
| 10 and 106 | 530 |
| 119 and 141 | 16779 |
| 42 and 51 | 714 |