Least Common Multiple (LCM) of 182 and 112
The least common multiple (LCM) of 182 and 112 is 1456.
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 182 and 112?
First, calculate the GCD of 182 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 182 ÷ 112 = 1 remainder 70 |
| 2 | 112 ÷ 70 = 1 remainder 42 |
| 3 | 70 ÷ 42 = 1 remainder 28 |
| 4 | 42 ÷ 28 = 1 remainder 14 |
| 5 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 188 | 21244 |
| 121 and 100 | 12100 |
| 188 and 14 | 1316 |
| 141 and 177 | 8319 |
| 20 and 173 | 3460 |