Least Common Multiple (LCM) of 112 and 43
The least common multiple (LCM) of 112 and 43 is 4816.
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 43?
First, calculate the GCD of 112 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 43 = 2 remainder 26 |
| 2 | 43 ÷ 26 = 1 remainder 17 |
| 3 | 26 ÷ 17 = 1 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 193 | 11194 |
| 164 and 46 | 3772 |
| 61 and 165 | 10065 |
| 193 and 170 | 32810 |
| 114 and 21 | 798 |