Least Common Multiple (LCM) of 180 and 71
The least common multiple (LCM) of 180 and 71 is 12780.
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 180 and 71?
First, calculate the GCD of 180 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 71 = 2 remainder 38 |
| 2 | 71 ÷ 38 = 1 remainder 33 |
| 3 | 38 ÷ 33 = 1 remainder 5 |
| 4 | 33 ÷ 5 = 6 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 189 | 378 |
| 150 and 147 | 7350 |
| 83 and 43 | 3569 |
| 127 and 67 | 8509 |
| 186 and 94 | 8742 |