Least Common Multiple (LCM) of 112 and 192
The least common multiple (LCM) of 112 and 192 is 1344.
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 192?
First, calculate the GCD of 112 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 192 = 0 remainder 112 |
| 2 | 192 ÷ 112 = 1 remainder 80 |
| 3 | 112 ÷ 80 = 1 remainder 32 |
| 4 | 80 ÷ 32 = 2 remainder 16 |
| 5 | 32 ÷ 16 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 13 | 2288 |
| 122 and 160 | 9760 |
| 159 and 83 | 13197 |
| 159 and 133 | 21147 |
| 100 and 18 | 900 |