Least Common Multiple (LCM) of 47 and 112
The least common multiple (LCM) of 47 and 112 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 47 and 112?
First, calculate the GCD of 47 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 112 = 0 remainder 47 |
| 2 | 112 ÷ 47 = 2 remainder 18 |
| 3 | 47 ÷ 18 = 2 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 96 | 13920 |
| 169 and 64 | 10816 |
| 78 and 198 | 2574 |
| 196 and 199 | 39004 |
| 78 and 157 | 12246 |