Least Common Multiple (LCM) of 127 and 171
The least common multiple (LCM) of 127 and 171 is 21717.
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 127 and 171?
First, calculate the GCD of 127 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 171 = 0 remainder 127 |
| 2 | 171 ÷ 127 = 1 remainder 44 |
| 3 | 127 ÷ 44 = 2 remainder 39 |
| 4 | 44 ÷ 39 = 1 remainder 5 |
| 5 | 39 ÷ 5 = 7 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 138 | 8970 |
| 74 and 103 | 7622 |
| 80 and 14 | 560 |
| 86 and 97 | 8342 |
| 44 and 181 | 7964 |