Least Common Multiple (LCM) of 55 and 135
The least common multiple (LCM) of 55 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 55 and 135?
First, calculate the GCD of 55 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 135 = 0 remainder 55 |
| 2 | 135 ÷ 55 = 2 remainder 25 |
| 3 | 55 ÷ 25 = 2 remainder 5 |
| 4 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 85 | 14365 |
| 135 and 21 | 945 |
| 116 and 58 | 116 |
| 176 and 168 | 3696 |
| 110 and 67 | 7370 |