Least Common Multiple (LCM) of 189 and 66
The least common multiple (LCM) of 189 and 66 is 4158.
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 66?
First, calculate the GCD of 189 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 66 = 2 remainder 57 |
| 2 | 66 ÷ 57 = 1 remainder 9 |
| 3 | 57 ÷ 9 = 6 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 72 | 72 |
| 37 and 106 | 3922 |
| 142 and 171 | 24282 |
| 177 and 46 | 8142 |
| 184 and 48 | 1104 |