Least Common Multiple (LCM) of 71 and 138
The least common multiple (LCM) of 71 and 138 is 9798.
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 138?
First, calculate the GCD of 71 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 138 = 0 remainder 71 |
| 2 | 138 ÷ 71 = 1 remainder 67 |
| 3 | 71 ÷ 67 = 1 remainder 4 |
| 4 | 67 ÷ 4 = 16 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 103 | 13287 |
| 146 and 36 | 2628 |
| 40 and 80 | 80 |
| 198 and 44 | 396 |
| 168 and 127 | 21336 |