Least Common Multiple (LCM) of 107 and 182
The least common multiple (LCM) of 107 and 182 is 19474.
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 107 and 182?
First, calculate the GCD of 107 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 182 = 0 remainder 107 |
| 2 | 182 ÷ 107 = 1 remainder 75 |
| 3 | 107 ÷ 75 = 1 remainder 32 |
| 4 | 75 ÷ 32 = 2 remainder 11 |
| 5 | 32 ÷ 11 = 2 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 173 | 22663 |
| 105 and 30 | 210 |
| 168 and 125 | 21000 |
| 124 and 198 | 12276 |
| 21 and 168 | 168 |