Least Common Multiple (LCM) of 31 and 19
The least common multiple (LCM) of 31 and 19 is 589.
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 19?
First, calculate the GCD of 31 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 19 = 1 remainder 12 |
| 2 | 19 ÷ 12 = 1 remainder 7 |
| 3 | 12 ÷ 7 = 1 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 77 | 12243 |
| 81 and 17 | 1377 |
| 64 and 140 | 2240 |
| 128 and 53 | 6784 |
| 120 and 123 | 4920 |