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 |
|---|---|
| 126 and 41 | 5166 |
| 180 and 146 | 13140 |
| 112 and 61 | 6832 |
| 157 and 39 | 6123 |
| 164 and 50 | 4100 |