Least Common Multiple (LCM) of 48 and 135
The least common multiple (LCM) of 48 and 135 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 48 and 135?
First, calculate the GCD of 48 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 135 = 0 remainder 48 |
| 2 | 135 ÷ 48 = 2 remainder 39 |
| 3 | 48 ÷ 39 = 1 remainder 9 |
| 4 | 39 ÷ 9 = 4 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 125 | 2750 |
| 122 and 102 | 6222 |
| 178 and 64 | 5696 |
| 188 and 63 | 11844 |
| 175 and 81 | 14175 |