Least Common Multiple (LCM) of 31 and 28
The least common multiple (LCM) of 31 and 28 is 868.
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 28?
First, calculate the GCD of 31 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 28 = 1 remainder 3 |
| 2 | 28 ÷ 3 = 9 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 144 | 5904 |
| 14 and 140 | 140 |
| 190 and 126 | 11970 |
| 166 and 150 | 12450 |
| 68 and 31 | 2108 |