Least Common Multiple (LCM) of 169 and 128
The least common multiple (LCM) of 169 and 128 is 21632.
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 169 and 128?
First, calculate the GCD of 169 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 128 = 1 remainder 41 |
| 2 | 128 ÷ 41 = 3 remainder 5 |
| 3 | 41 ÷ 5 = 8 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 80 | 3120 |
| 133 and 34 | 4522 |
| 31 and 119 | 3689 |
| 134 and 104 | 6968 |
| 85 and 193 | 16405 |