Least Common Multiple (LCM) of 174 and 128
The least common multiple (LCM) of 174 and 128 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 174 and 128?
First, calculate the GCD of 174 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 128 = 1 remainder 46 |
| 2 | 128 ÷ 46 = 2 remainder 36 |
| 3 | 46 ÷ 36 = 1 remainder 10 |
| 4 | 36 ÷ 10 = 3 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 132 | 6996 |
| 109 and 49 | 5341 |
| 93 and 94 | 8742 |
| 152 and 123 | 18696 |
| 144 and 24 | 144 |