Least Common Multiple (LCM) of 32 and 189
The least common multiple (LCM) of 32 and 189 is 6048.
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 32 and 189?
First, calculate the GCD of 32 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 189 = 0 remainder 32 |
| 2 | 189 ÷ 32 = 5 remainder 29 |
| 3 | 32 ÷ 29 = 1 remainder 3 |
| 4 | 29 ÷ 3 = 9 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 31 | 4557 |
| 133 and 36 | 4788 |
| 151 and 11 | 1661 |
| 140 and 18 | 1260 |
| 117 and 100 | 11700 |