Least Common Multiple (LCM) of 189 and 178
The least common multiple (LCM) of 189 and 178 is 33642.
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 189 and 178?
First, calculate the GCD of 189 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 178 = 1 remainder 11 |
| 2 | 178 ÷ 11 = 16 remainder 2 |
| 3 | 11 ÷ 2 = 5 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 16 | 1712 |
| 102 and 128 | 6528 |
| 168 and 13 | 2184 |
| 12 and 49 | 588 |
| 142 and 77 | 10934 |