Least Common Multiple (LCM) of 111 and 106
The least common multiple (LCM) of 111 and 106 is 11766.
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 106?
First, calculate the GCD of 111 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 106 = 1 remainder 5 |
| 2 | 106 ÷ 5 = 21 remainder 1 |
| 3 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 131 | 25807 |
| 180 and 71 | 12780 |
| 41 and 27 | 1107 |
| 11 and 180 | 1980 |
| 29 and 158 | 4582 |