Least Common Multiple (LCM) of 31 and 171
The least common multiple (LCM) of 31 and 171 is 5301.
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 171?
First, calculate the GCD of 31 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 171 = 0 remainder 31 |
| 2 | 171 ÷ 31 = 5 remainder 16 |
| 3 | 31 ÷ 16 = 1 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 65 | 9945 |
| 163 and 92 | 14996 |
| 19 and 142 | 2698 |
| 113 and 63 | 7119 |
| 128 and 186 | 11904 |