Least Common Multiple (LCM) of 112 and 81
The least common multiple (LCM) of 112 and 81 is 9072.
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 81?
First, calculate the GCD of 112 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 81 = 1 remainder 31 |
| 2 | 81 ÷ 31 = 2 remainder 19 |
| 3 | 31 ÷ 19 = 1 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 74 | 3626 |
| 105 and 174 | 6090 |
| 164 and 106 | 8692 |
| 198 and 14 | 1386 |
| 136 and 100 | 3400 |