Least Common Multiple (LCM) of 126 and 71
The least common multiple (LCM) of 126 and 71 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 126 and 71?
First, calculate the GCD of 126 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 71 = 1 remainder 55 |
| 2 | 71 ÷ 55 = 1 remainder 16 |
| 3 | 55 ÷ 16 = 3 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 119 | 7021 |
| 173 and 126 | 21798 |
| 142 and 194 | 13774 |
| 99 and 68 | 6732 |
| 71 and 29 | 2059 |