Least Common Multiple (LCM) of 112 and 182
The least common multiple (LCM) of 112 and 182 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 112 and 182?
First, calculate the GCD of 112 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 182 = 0 remainder 112 |
| 2 | 182 ÷ 112 = 1 remainder 70 |
| 3 | 112 ÷ 70 = 1 remainder 42 |
| 4 | 70 ÷ 42 = 1 remainder 28 |
| 5 | 42 ÷ 28 = 1 remainder 14 |
| 6 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 137 | 14659 |
| 32 and 97 | 3104 |
| 189 and 106 | 20034 |
| 136 and 60 | 2040 |
| 124 and 70 | 4340 |