Least Common Multiple (LCM) of 31 and 177
The least common multiple (LCM) of 31 and 177 is 5487.
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 177?
First, calculate the GCD of 31 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 177 = 0 remainder 31 |
| 2 | 177 ÷ 31 = 5 remainder 22 |
| 3 | 31 ÷ 22 = 1 remainder 9 |
| 4 | 22 ÷ 9 = 2 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 154 | 1540 |
| 112 and 32 | 224 |
| 133 and 182 | 3458 |
| 14 and 101 | 1414 |
| 32 and 160 | 160 |