Least Common Multiple (LCM) of 189 and 41
The least common multiple (LCM) of 189 and 41 is 7749.
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 41?
First, calculate the GCD of 189 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 41 = 4 remainder 25 |
| 2 | 41 ÷ 25 = 1 remainder 16 |
| 3 | 25 ÷ 16 = 1 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 73 | 9344 |
| 33 and 35 | 1155 |
| 77 and 118 | 9086 |
| 65 and 196 | 12740 |
| 35 and 178 | 6230 |