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 |
|---|---|
| 53 and 153 | 8109 |
| 14 and 138 | 966 |
| 105 and 129 | 4515 |
| 101 and 27 | 2727 |
| 110 and 125 | 2750 |