Least Common Multiple (LCM) of 109 and 182
The least common multiple (LCM) of 109 and 182 is 19838.
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 109 and 182?
First, calculate the GCD of 109 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 182 = 0 remainder 109 |
| 2 | 182 ÷ 109 = 1 remainder 73 |
| 3 | 109 ÷ 73 = 1 remainder 36 |
| 4 | 73 ÷ 36 = 2 remainder 1 |
| 5 | 36 ÷ 1 = 36 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 115 | 17710 |
| 38 and 188 | 3572 |
| 168 and 13 | 2184 |
| 41 and 194 | 7954 |
| 75 and 188 | 14100 |