Least Common Multiple (LCM) of 128 and 135
The least common multiple (LCM) of 128 and 135 is 17280.
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 128 and 135?
First, calculate the GCD of 128 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 135 = 0 remainder 128 |
| 2 | 135 ÷ 128 = 1 remainder 7 |
| 3 | 128 ÷ 7 = 18 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 40 | 680 |
| 161 and 10 | 1610 |
| 56 and 124 | 1736 |
| 137 and 71 | 9727 |
| 137 and 103 | 14111 |