Least Common Multiple (LCM) of 71 and 177
The least common multiple (LCM) of 71 and 177 is 12567.
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 71 and 177?
First, calculate the GCD of 71 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 177 = 0 remainder 71 |
| 2 | 177 ÷ 71 = 2 remainder 35 |
| 3 | 71 ÷ 35 = 2 remainder 1 |
| 4 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 39 | 4134 |
| 121 and 73 | 8833 |
| 24 and 131 | 3144 |
| 36 and 38 | 684 |
| 54 and 117 | 702 |