Least Common Multiple (LCM) of 96 and 135
The least common multiple (LCM) of 96 and 135 is 4320.
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 96 and 135?
First, calculate the GCD of 96 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 135 = 0 remainder 96 |
| 2 | 135 ÷ 96 = 1 remainder 39 |
| 3 | 96 ÷ 39 = 2 remainder 18 |
| 4 | 39 ÷ 18 = 2 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 43 | 5160 |
| 22 and 43 | 946 |
| 180 and 128 | 5760 |
| 15 and 104 | 1560 |
| 21 and 33 | 231 |