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 |
|---|---|
| 177 and 77 | 13629 |
| 96 and 94 | 4512 |
| 120 and 83 | 9960 |
| 160 and 127 | 20320 |
| 141 and 124 | 17484 |