Least Common Multiple (LCM) of 12 and 32
The least common multiple (LCM) of 12 and 32 is 96.
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 12 and 32?
First, calculate the GCD of 12 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 32 = 0 remainder 12 |
| 2 | 32 ÷ 12 = 2 remainder 8 |
| 3 | 12 ÷ 8 = 1 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 11 | 2145 |
| 132 and 107 | 14124 |
| 46 and 166 | 3818 |
| 78 and 88 | 3432 |
| 175 and 44 | 7700 |