Least Common Multiple (LCM) of 128 and 90
The least common multiple (LCM) of 128 and 90 is 5760.
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 90?
First, calculate the GCD of 128 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 90 = 1 remainder 38 |
| 2 | 90 ÷ 38 = 2 remainder 14 |
| 3 | 38 ÷ 14 = 2 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 123 | 3444 |
| 175 and 89 | 15575 |
| 120 and 174 | 3480 |
| 85 and 31 | 2635 |
| 154 and 15 | 2310 |