Least Common Multiple (LCM) of 183 and 112
The least common multiple (LCM) of 183 and 112 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 183 and 112?
First, calculate the GCD of 183 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 183 ÷ 112 = 1 remainder 71 |
| 2 | 112 ÷ 71 = 1 remainder 41 |
| 3 | 71 ÷ 41 = 1 remainder 30 |
| 4 | 41 ÷ 30 = 1 remainder 11 |
| 5 | 30 ÷ 11 = 2 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 100 | 5300 |
| 173 and 88 | 15224 |
| 69 and 97 | 6693 |
| 165 and 119 | 19635 |
| 123 and 180 | 7380 |