Least Common Multiple (LCM) of 18 and 32
The least common multiple (LCM) of 18 and 32 is 288.
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 18 and 32?
First, calculate the GCD of 18 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 32 = 0 remainder 18 |
| 2 | 32 ÷ 18 = 1 remainder 14 |
| 3 | 18 ÷ 14 = 1 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 77 | 8393 |
| 20 and 161 | 3220 |
| 35 and 192 | 6720 |
| 187 and 137 | 25619 |
| 101 and 131 | 13231 |