Least Common Multiple (LCM) of 135 and 165
The least common multiple (LCM) of 135 and 165 is 1485.
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 165?
First, calculate the GCD of 135 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 165 = 0 remainder 135 |
| 2 | 165 ÷ 135 = 1 remainder 30 |
| 3 | 135 ÷ 30 = 4 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 89 | 10235 |
| 168 and 69 | 3864 |
| 124 and 87 | 10788 |
| 39 and 190 | 7410 |
| 169 and 25 | 4225 |