Least Common Multiple (LCM) of 115 and 31
The least common multiple (LCM) of 115 and 31 is 3565.
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 115 and 31?
First, calculate the GCD of 115 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 31 = 3 remainder 22 |
| 2 | 31 ÷ 22 = 1 remainder 9 |
| 3 | 22 ÷ 9 = 2 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 92 | 3864 |
| 98 and 159 | 15582 |
| 48 and 133 | 6384 |
| 170 and 125 | 4250 |
| 147 and 144 | 7056 |