Least Common Multiple (LCM) of 135 and 96
The least common multiple (LCM) of 135 and 96 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 135 and 96?
First, calculate the GCD of 135 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 96 = 1 remainder 39 |
| 2 | 96 ÷ 39 = 2 remainder 18 |
| 3 | 39 ÷ 18 = 2 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 170 | 14620 |
| 36 and 101 | 3636 |
| 165 and 74 | 12210 |
| 81 and 44 | 3564 |
| 13 and 36 | 468 |