Least Common Multiple (LCM) of 128 and 175
The least common multiple (LCM) of 128 and 175 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 128 and 175?
First, calculate the GCD of 128 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 175 = 0 remainder 128 |
| 2 | 175 ÷ 128 = 1 remainder 47 |
| 3 | 128 ÷ 47 = 2 remainder 34 |
| 4 | 47 ÷ 34 = 1 remainder 13 |
| 5 | 34 ÷ 13 = 2 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 86 | 8514 |
| 112 and 113 | 12656 |
| 32 and 68 | 544 |
| 63 and 87 | 1827 |
| 16 and 97 | 1552 |