Least Common Multiple (LCM) of 31 and 43
The least common multiple (LCM) of 31 and 43 is 1333.
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 43?
First, calculate the GCD of 31 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 43 = 0 remainder 31 |
| 2 | 43 ÷ 31 = 1 remainder 12 |
| 3 | 31 ÷ 12 = 2 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 83 | 9711 |
| 58 and 88 | 2552 |
| 16 and 198 | 1584 |
| 131 and 67 | 8777 |
| 194 and 63 | 12222 |