Least Common Multiple (LCM) of 71 and 127
The least common multiple (LCM) of 71 and 127 is 9017.
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 127?
First, calculate the GCD of 71 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 127 = 0 remainder 71 |
| 2 | 127 ÷ 71 = 1 remainder 56 |
| 3 | 71 ÷ 56 = 1 remainder 15 |
| 4 | 56 ÷ 15 = 3 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 151 | 19328 |
| 181 and 114 | 20634 |
| 122 and 66 | 4026 |
| 21 and 75 | 525 |
| 114 and 92 | 5244 |