Least Common Multiple (LCM) of 171 and 111
The least common multiple (LCM) of 171 and 111 is 6327.
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 111?
First, calculate the GCD of 171 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 111 = 1 remainder 60 |
| 2 | 111 ÷ 60 = 1 remainder 51 |
| 3 | 60 ÷ 51 = 1 remainder 9 |
| 4 | 51 ÷ 9 = 5 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 10 | 130 |
| 37 and 78 | 2886 |
| 14 and 100 | 700 |
| 139 and 106 | 14734 |
| 190 and 45 | 1710 |