Least Common Multiple (LCM) of 31 and 128
The least common multiple (LCM) of 31 and 128 is 3968.
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 128?
First, calculate the GCD of 31 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 128 = 0 remainder 31 |
| 2 | 128 ÷ 31 = 4 remainder 4 |
| 3 | 31 ÷ 4 = 7 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 172 | 3440 |
| 133 and 75 | 9975 |
| 118 and 45 | 5310 |
| 29 and 45 | 1305 |
| 31 and 54 | 1674 |