Least Common Multiple (LCM) of 171 and 31
The least common multiple (LCM) of 171 and 31 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 171 and 31?
First, calculate the GCD of 171 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 31 = 5 remainder 16 |
| 2 | 31 ÷ 16 = 1 remainder 15 |
| 3 | 16 ÷ 15 = 1 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 96 | 3360 |
| 180 and 199 | 35820 |
| 11 and 104 | 1144 |
| 77 and 90 | 6930 |
| 163 and 61 | 9943 |