Least Common Multiple (LCM) of 71 and 139
The least common multiple (LCM) of 71 and 139 is 9869.
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 139?
First, calculate the GCD of 71 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 139 = 0 remainder 71 |
| 2 | 139 ÷ 71 = 1 remainder 68 |
| 3 | 71 ÷ 68 = 1 remainder 3 |
| 4 | 68 ÷ 3 = 22 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 79 | 7900 |
| 169 and 18 | 3042 |
| 125 and 183 | 22875 |
| 107 and 20 | 2140 |
| 144 and 196 | 7056 |