Least Common Multiple (LCM) of 128 and 174
The least common multiple (LCM) of 128 and 174 is 11136.
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 174?
First, calculate the GCD of 128 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 174 = 0 remainder 128 |
| 2 | 174 ÷ 128 = 1 remainder 46 |
| 3 | 128 ÷ 46 = 2 remainder 36 |
| 4 | 46 ÷ 36 = 1 remainder 10 |
| 5 | 36 ÷ 10 = 3 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 138 | 6210 |
| 34 and 165 | 5610 |
| 120 and 160 | 480 |
| 200 and 122 | 12200 |
| 147 and 103 | 15141 |