Least Common Multiple (LCM) of 191 and 112
The least common multiple (LCM) of 191 and 112 is 21392.
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 191 and 112?
First, calculate the GCD of 191 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 112 = 1 remainder 79 |
| 2 | 112 ÷ 79 = 1 remainder 33 |
| 3 | 79 ÷ 33 = 2 remainder 13 |
| 4 | 33 ÷ 13 = 2 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 179 | 14678 |
| 149 and 157 | 23393 |
| 192 and 128 | 384 |
| 178 and 192 | 17088 |
| 144 and 147 | 7056 |