Least Common Multiple (LCM) of 165 and 135
The least common multiple (LCM) of 165 and 135 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 165 and 135?
First, calculate the GCD of 165 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 135 = 1 remainder 30 |
| 2 | 135 ÷ 30 = 4 remainder 15 |
| 3 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 98 | 1078 |
| 123 and 119 | 14637 |
| 21 and 105 | 105 |
| 47 and 133 | 6251 |
| 199 and 84 | 16716 |