Least Common Multiple (LCM) of 12 and 47
The least common multiple (LCM) of 12 and 47 is 564.
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 47?
First, calculate the GCD of 12 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 47 = 0 remainder 12 |
| 2 | 47 ÷ 12 = 3 remainder 11 |
| 3 | 12 ÷ 11 = 1 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 163 | 13529 |
| 108 and 40 | 1080 |
| 56 and 24 | 168 |
| 167 and 169 | 28223 |
| 19 and 36 | 684 |