Least Common Multiple (LCM) of 71 and 140
The least common multiple (LCM) of 71 and 140 is 9940.
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 140?
First, calculate the GCD of 71 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 140 = 0 remainder 71 |
| 2 | 140 ÷ 71 = 1 remainder 69 |
| 3 | 71 ÷ 69 = 1 remainder 2 |
| 4 | 69 ÷ 2 = 34 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 63 | 12159 |
| 115 and 186 | 21390 |
| 23 and 71 | 1633 |
| 185 and 100 | 3700 |
| 188 and 198 | 18612 |