Least Common Multiple (LCM) of 128 and 69
The least common multiple (LCM) of 128 and 69 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 128 and 69?
First, calculate the GCD of 128 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 69 = 1 remainder 59 |
| 2 | 69 ÷ 59 = 1 remainder 10 |
| 3 | 59 ÷ 10 = 5 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 144 | 25200 |
| 72 and 32 | 288 |
| 175 and 99 | 17325 |
| 80 and 151 | 12080 |
| 68 and 100 | 1700 |