Least Common Multiple (LCM) of 31 and 80
The least common multiple (LCM) of 31 and 80 is 2480.
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 80?
First, calculate the GCD of 31 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 80 = 0 remainder 31 |
| 2 | 80 ÷ 31 = 2 remainder 18 |
| 3 | 31 ÷ 18 = 1 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 52 | 8580 |
| 152 and 82 | 6232 |
| 34 and 14 | 238 |
| 98 and 182 | 1274 |
| 196 and 139 | 27244 |