Least Common Multiple (LCM) of 175 and 128
The least common multiple (LCM) of 175 and 128 is 22400.
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 175 and 128?
First, calculate the GCD of 175 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 128 = 1 remainder 47 |
| 2 | 128 ÷ 47 = 2 remainder 34 |
| 3 | 47 ÷ 34 = 1 remainder 13 |
| 4 | 34 ÷ 13 = 2 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 114 | 4674 |
| 196 and 51 | 9996 |
| 33 and 42 | 462 |
| 106 and 23 | 2438 |
| 165 and 49 | 8085 |