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 |
|---|---|
| 180 and 173 | 31140 |
| 106 and 101 | 10706 |
| 126 and 57 | 2394 |
| 114 and 38 | 114 |
| 11 and 77 | 77 |