Least Common Multiple (LCM) of 128 and 99
The least common multiple (LCM) of 128 and 99 is 12672.
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 99?
First, calculate the GCD of 128 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 99 = 1 remainder 29 |
| 2 | 99 ÷ 29 = 3 remainder 12 |
| 3 | 29 ÷ 12 = 2 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 11 | 1100 |
| 27 and 159 | 1431 |
| 84 and 138 | 1932 |
| 176 and 55 | 880 |
| 61 and 97 | 5917 |