Least Common Multiple (LCM) of 135 and 177
The least common multiple (LCM) of 135 and 177 is 7965.
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 135 and 177?
First, calculate the GCD of 135 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 177 = 0 remainder 135 |
| 2 | 177 ÷ 135 = 1 remainder 42 |
| 3 | 135 ÷ 42 = 3 remainder 9 |
| 4 | 42 ÷ 9 = 4 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 197 | 8865 |
| 129 and 14 | 1806 |
| 142 and 137 | 19454 |
| 85 and 189 | 16065 |
| 169 and 25 | 4225 |