Least Common Multiple (LCM) of 178 and 96
The least common multiple (LCM) of 178 and 96 is 8544.
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 96?
First, calculate the GCD of 178 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 96 = 1 remainder 82 |
| 2 | 96 ÷ 82 = 1 remainder 14 |
| 3 | 82 ÷ 14 = 5 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 33 | 660 |
| 191 and 24 | 4584 |
| 160 and 61 | 9760 |
| 29 and 105 | 3045 |
| 27 and 128 | 3456 |