Least Common Multiple (LCM) of 111 and 117
The least common multiple (LCM) of 111 and 117 is 4329.
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 117?
First, calculate the GCD of 111 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 117 = 0 remainder 111 |
| 2 | 117 ÷ 111 = 1 remainder 6 |
| 3 | 111 ÷ 6 = 18 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 53 | 8533 |
| 177 and 82 | 14514 |
| 69 and 29 | 2001 |
| 185 and 181 | 33485 |
| 67 and 77 | 5159 |