Least Common Multiple (LCM) of 111 and 177
The least common multiple (LCM) of 111 and 177 is 6549.
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 177?
First, calculate the GCD of 111 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 177 = 0 remainder 111 |
| 2 | 177 ÷ 111 = 1 remainder 66 |
| 3 | 111 ÷ 66 = 1 remainder 45 |
| 4 | 66 ÷ 45 = 1 remainder 21 |
| 5 | 45 ÷ 21 = 2 remainder 3 |
| 6 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 67 | 3618 |
| 30 and 109 | 3270 |
| 194 and 141 | 27354 |
| 165 and 32 | 5280 |
| 77 and 120 | 9240 |