Least Common Multiple (LCM) of 111 and 176
The least common multiple (LCM) of 111 and 176 is 19536.
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 176?
First, calculate the GCD of 111 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 176 = 0 remainder 111 |
| 2 | 176 ÷ 111 = 1 remainder 65 |
| 3 | 111 ÷ 65 = 1 remainder 46 |
| 4 | 65 ÷ 46 = 1 remainder 19 |
| 5 | 46 ÷ 19 = 2 remainder 8 |
| 6 | 19 ÷ 8 = 2 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 105 | 1785 |
| 115 and 39 | 4485 |
| 173 and 17 | 2941 |
| 77 and 130 | 10010 |
| 56 and 136 | 952 |