Least Common Multiple (LCM) of 112 and 47
The least common multiple (LCM) of 112 and 47 is 5264.
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 112 and 47?
First, calculate the GCD of 112 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 47 = 2 remainder 18 |
| 2 | 47 ÷ 18 = 2 remainder 11 |
| 3 | 18 ÷ 11 = 1 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 142 | 3266 |
| 15 and 31 | 465 |
| 101 and 108 | 10908 |
| 172 and 51 | 8772 |
| 71 and 59 | 4189 |