Least Common Multiple (LCM) of 128 and 169
The least common multiple (LCM) of 128 and 169 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 128 and 169?
First, calculate the GCD of 128 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 169 = 0 remainder 128 |
| 2 | 169 ÷ 128 = 1 remainder 41 |
| 3 | 128 ÷ 41 = 3 remainder 5 |
| 4 | 41 ÷ 5 = 8 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 62 | 620 |
| 82 and 23 | 1886 |
| 19 and 196 | 3724 |
| 72 and 120 | 360 |
| 164 and 109 | 17876 |