Least Common Multiple (LCM) of 31 and 115
The least common multiple (LCM) of 31 and 115 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 31 and 115?
First, calculate the GCD of 31 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 115 = 0 remainder 31 |
| 2 | 115 ÷ 31 = 3 remainder 22 |
| 3 | 31 ÷ 22 = 1 remainder 9 |
| 4 | 22 ÷ 9 = 2 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 63 | 1260 |
| 175 and 140 | 700 |
| 102 and 77 | 7854 |
| 153 and 55 | 8415 |
| 85 and 42 | 3570 |