Least Common Multiple (LCM) of 128 and 178
The least common multiple (LCM) of 128 and 178 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 128 and 178?
First, calculate the GCD of 128 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 178 = 0 remainder 128 |
| 2 | 178 ÷ 128 = 1 remainder 50 |
| 3 | 128 ÷ 50 = 2 remainder 28 |
| 4 | 50 ÷ 28 = 1 remainder 22 |
| 5 | 28 ÷ 22 = 1 remainder 6 |
| 6 | 22 ÷ 6 = 3 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 167 | 5344 |
| 96 and 57 | 1824 |
| 66 and 64 | 2112 |
| 120 and 67 | 8040 |
| 10 and 134 | 670 |