Least Common Multiple (LCM) of 180 and 31
The least common multiple (LCM) of 180 and 31 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 180 and 31?
First, calculate the GCD of 180 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 31 = 5 remainder 25 |
| 2 | 31 ÷ 25 = 1 remainder 6 |
| 3 | 25 ÷ 6 = 4 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 116 | 7540 |
| 69 and 124 | 8556 |
| 190 and 54 | 5130 |
| 127 and 56 | 7112 |
| 113 and 31 | 3503 |