Least Common Multiple (LCM) of 135 and 48
The least common multiple (LCM) of 135 and 48 is 2160.
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 48?
First, calculate the GCD of 135 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 48 = 2 remainder 39 |
| 2 | 48 ÷ 39 = 1 remainder 9 |
| 3 | 39 ÷ 9 = 4 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 75 | 6600 |
| 14 and 117 | 1638 |
| 68 and 167 | 11356 |
| 149 and 88 | 13112 |
| 147 and 156 | 7644 |