Least Common Multiple (LCM) of 112 and 191
The least common multiple (LCM) of 112 and 191 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 112 and 191?
First, calculate the GCD of 112 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 191 = 0 remainder 112 |
| 2 | 191 ÷ 112 = 1 remainder 79 |
| 3 | 112 ÷ 79 = 1 remainder 33 |
| 4 | 79 ÷ 33 = 2 remainder 13 |
| 5 | 33 ÷ 13 = 2 remainder 7 |
| 6 | 13 ÷ 7 = 1 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 77 | 77 |
| 70 and 150 | 1050 |
| 66 and 14 | 462 |
| 99 and 144 | 1584 |
| 96 and 77 | 7392 |