Least Common Multiple (LCM) of 54 and 177
The least common multiple (LCM) of 54 and 177 is 3186.
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 54 and 177?
First, calculate the GCD of 54 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 177 = 0 remainder 54 |
| 2 | 177 ÷ 54 = 3 remainder 15 |
| 3 | 54 ÷ 15 = 3 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 112 | 112 |
| 94 and 98 | 4606 |
| 198 and 12 | 396 |
| 18 and 84 | 252 |
| 131 and 113 | 14803 |