Least Common Multiple (LCM) of 192 and 112
The least common multiple (LCM) of 192 and 112 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 192 and 112?
First, calculate the GCD of 192 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 112 = 1 remainder 80 |
| 2 | 112 ÷ 80 = 1 remainder 32 |
| 3 | 80 ÷ 32 = 2 remainder 16 |
| 4 | 32 ÷ 16 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 132 | 660 |
| 149 and 161 | 23989 |
| 31 and 113 | 3503 |
| 87 and 17 | 1479 |
| 40 and 195 | 1560 |