Least Common Multiple (LCM) of 112 and 184
The least common multiple (LCM) of 112 and 184 is 2576.
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 184?
First, calculate the GCD of 112 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 184 = 0 remainder 112 |
| 2 | 184 ÷ 112 = 1 remainder 72 |
| 3 | 112 ÷ 72 = 1 remainder 40 |
| 4 | 72 ÷ 40 = 1 remainder 32 |
| 5 | 40 ÷ 32 = 1 remainder 8 |
| 6 | 32 ÷ 8 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 84 | 4956 |
| 67 and 10 | 670 |
| 18 and 104 | 936 |
| 128 and 183 | 23424 |
| 149 and 161 | 23989 |