Least Common Multiple (LCM) of 71 and 126
The least common multiple (LCM) of 71 and 126 is 8946.
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 126?
First, calculate the GCD of 71 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 126 = 0 remainder 71 |
| 2 | 126 ÷ 71 = 1 remainder 55 |
| 3 | 71 ÷ 55 = 1 remainder 16 |
| 4 | 55 ÷ 16 = 3 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 66 | 1980 |
| 22 and 149 | 3278 |
| 55 and 19 | 1045 |
| 35 and 171 | 5985 |
| 47 and 158 | 7426 |