Least Common Multiple (LCM) of 13 and 128
The least common multiple (LCM) of 13 and 128 is 1664.
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 13 and 128?
First, calculate the GCD of 13 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 128 = 0 remainder 13 |
| 2 | 128 ÷ 13 = 9 remainder 11 |
| 3 | 13 ÷ 11 = 1 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 101 | 12019 |
| 110 and 106 | 5830 |
| 174 and 15 | 870 |
| 163 and 96 | 15648 |
| 161 and 90 | 14490 |