Least Common Multiple (LCM) of 132 and 189
The least common multiple (LCM) of 132 and 189 is 8316.
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 132 and 189?
First, calculate the GCD of 132 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 189 = 0 remainder 132 |
| 2 | 189 ÷ 132 = 1 remainder 57 |
| 3 | 132 ÷ 57 = 2 remainder 18 |
| 4 | 57 ÷ 18 = 3 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 162 | 1620 |
| 160 and 120 | 480 |
| 48 and 109 | 5232 |
| 59 and 107 | 6313 |
| 178 and 173 | 30794 |