Least Common Multiple (LCM) of 110 and 177
The least common multiple (LCM) of 110 and 177 is 19470.
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 110 and 177?
First, calculate the GCD of 110 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 177 = 0 remainder 110 |
| 2 | 177 ÷ 110 = 1 remainder 67 |
| 3 | 110 ÷ 67 = 1 remainder 43 |
| 4 | 67 ÷ 43 = 1 remainder 24 |
| 5 | 43 ÷ 24 = 1 remainder 19 |
| 6 | 24 ÷ 19 = 1 remainder 5 |
| 7 | 19 ÷ 5 = 3 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 107 | 1819 |
| 174 and 76 | 6612 |
| 135 and 138 | 6210 |
| 112 and 133 | 2128 |
| 171 and 82 | 14022 |