Least Common Multiple (LCM) of 178 and 128
The least common multiple (LCM) of 178 and 128 is 11392.
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 178 and 128?
First, calculate the GCD of 178 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 128 = 1 remainder 50 |
| 2 | 128 ÷ 50 = 2 remainder 28 |
| 3 | 50 ÷ 28 = 1 remainder 22 |
| 4 | 28 ÷ 22 = 1 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 136 | 7752 |
| 46 and 24 | 552 |
| 189 and 114 | 7182 |
| 27 and 66 | 594 |
| 148 and 12 | 444 |