Least Common Multiple (LCM) of 90 and 128
The least common multiple (LCM) of 90 and 128 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 90 and 128?
First, calculate the GCD of 90 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 128 = 0 remainder 90 |
| 2 | 128 ÷ 90 = 1 remainder 38 |
| 3 | 90 ÷ 38 = 2 remainder 14 |
| 4 | 38 ÷ 14 = 2 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 169 | 26871 |
| 32 and 10 | 160 |
| 43 and 135 | 5805 |
| 117 and 120 | 4680 |
| 163 and 130 | 21190 |