Least Common Multiple (LCM) of 177 and 111
The least common multiple (LCM) of 177 and 111 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 177 and 111?
First, calculate the GCD of 177 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 111 = 1 remainder 66 |
| 2 | 111 ÷ 66 = 1 remainder 45 |
| 3 | 66 ÷ 45 = 1 remainder 21 |
| 4 | 45 ÷ 21 = 2 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 47 | 1786 |
| 10 and 115 | 230 |
| 140 and 16 | 560 |
| 55 and 161 | 8855 |
| 127 and 142 | 18034 |