Least Common Multiple (LCM) of 112 and 183
The least common multiple (LCM) of 112 and 183 is 20496.
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 183?
First, calculate the GCD of 112 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 183 = 0 remainder 112 |
| 2 | 183 ÷ 112 = 1 remainder 71 |
| 3 | 112 ÷ 71 = 1 remainder 41 |
| 4 | 71 ÷ 41 = 1 remainder 30 |
| 5 | 41 ÷ 30 = 1 remainder 11 |
| 6 | 30 ÷ 11 = 2 remainder 8 |
| 7 | 11 ÷ 8 = 1 remainder 3 |
| 8 | 8 ÷ 3 = 2 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 14 | 112 |
| 90 and 17 | 1530 |
| 182 and 126 | 1638 |
| 103 and 76 | 7828 |
| 152 and 163 | 24776 |