Least Common Multiple (LCM) of 71 and 179
The least common multiple (LCM) of 71 and 179 is 12709.
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 179?
First, calculate the GCD of 71 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 179 = 0 remainder 71 |
| 2 | 179 ÷ 71 = 2 remainder 37 |
| 3 | 71 ÷ 37 = 1 remainder 34 |
| 4 | 37 ÷ 34 = 1 remainder 3 |
| 5 | 34 ÷ 3 = 11 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 179 | 20406 |
| 174 and 138 | 4002 |
| 12 and 37 | 444 |
| 152 and 141 | 21432 |
| 188 and 68 | 3196 |