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 |
|---|---|
| 106 and 33 | 3498 |
| 105 and 121 | 12705 |
| 17 and 106 | 1802 |
| 88 and 105 | 9240 |
| 132 and 185 | 24420 |