Least Common Multiple (LCM) of 31 and 182
The least common multiple (LCM) of 31 and 182 is 5642.
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 182?
First, calculate the GCD of 31 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 182 = 0 remainder 31 |
| 2 | 182 ÷ 31 = 5 remainder 27 |
| 3 | 31 ÷ 27 = 1 remainder 4 |
| 4 | 27 ÷ 4 = 6 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 161 | 17549 |
| 63 and 147 | 441 |
| 141 and 98 | 13818 |
| 49 and 59 | 2891 |
| 96 and 167 | 16032 |