Least Common Multiple (LCM) of 69 and 128
The least common multiple (LCM) of 69 and 128 is 8832.
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 69 and 128?
First, calculate the GCD of 69 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 128 = 0 remainder 69 |
| 2 | 128 ÷ 69 = 1 remainder 59 |
| 3 | 69 ÷ 59 = 1 remainder 10 |
| 4 | 59 ÷ 10 = 5 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 105 | 9030 |
| 40 and 17 | 680 |
| 166 and 105 | 17430 |
| 20 and 18 | 180 |
| 171 and 31 | 5301 |