Least Common Multiple (LCM) of 111 and 171
The least common multiple (LCM) of 111 and 171 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 111 and 171?
First, calculate the GCD of 111 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 171 = 0 remainder 111 |
| 2 | 171 ÷ 111 = 1 remainder 60 |
| 3 | 111 ÷ 60 = 1 remainder 51 |
| 4 | 60 ÷ 51 = 1 remainder 9 |
| 5 | 51 ÷ 9 = 5 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 29 | 3683 |
| 23 and 81 | 1863 |
| 62 and 138 | 4278 |
| 72 and 117 | 936 |
| 119 and 111 | 13209 |