Least Common Multiple (LCM) of 127 and 71
The least common multiple (LCM) of 127 and 71 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 127 and 71?
First, calculate the GCD of 127 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 71 = 1 remainder 56 |
| 2 | 71 ÷ 56 = 1 remainder 15 |
| 3 | 56 ÷ 15 = 3 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 56 | 6440 |
| 57 and 25 | 1425 |
| 53 and 183 | 9699 |
| 155 and 96 | 14880 |
| 187 and 114 | 21318 |