Least Common Multiple (LCM) of 189 and 32
The least common multiple (LCM) of 189 and 32 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 189 and 32?
First, calculate the GCD of 189 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 32 = 5 remainder 29 |
| 2 | 32 ÷ 29 = 1 remainder 3 |
| 3 | 29 ÷ 3 = 9 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 114 | 7410 |
| 142 and 133 | 18886 |
| 48 and 172 | 2064 |
| 120 and 162 | 3240 |
| 141 and 49 | 6909 |