Least Common Multiple (LCM) of 31 and 183
The least common multiple (LCM) of 31 and 183 is 5673.
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 31 and 183?
First, calculate the GCD of 31 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 183 = 0 remainder 31 |
| 2 | 183 ÷ 31 = 5 remainder 28 |
| 3 | 31 ÷ 28 = 1 remainder 3 |
| 4 | 28 ÷ 3 = 9 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 27 | 783 |
| 107 and 176 | 18832 |
| 84 and 141 | 3948 |
| 114 and 175 | 19950 |
| 25 and 81 | 2025 |