Least Common Multiple (LCM) of 27 and 177
The least common multiple (LCM) of 27 and 177 is 1593.
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 27 and 177?
First, calculate the GCD of 27 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 177 = 0 remainder 27 |
| 2 | 177 ÷ 27 = 6 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 90 | 540 |
| 122 and 36 | 2196 |
| 51 and 164 | 8364 |
| 64 and 90 | 2880 |
| 80 and 107 | 8560 |