Least Common Multiple (LCM) of 31 and 180
The least common multiple (LCM) of 31 and 180 is 5580.
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 31 and 180?
First, calculate the GCD of 31 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 180 = 0 remainder 31 |
| 2 | 180 ÷ 31 = 5 remainder 25 |
| 3 | 31 ÷ 25 = 1 remainder 6 |
| 4 | 25 ÷ 6 = 4 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 165 | 2145 |
| 186 and 147 | 9114 |
| 102 and 172 | 8772 |
| 101 and 200 | 20200 |
| 107 and 105 | 11235 |