Least Common Multiple (LCM) of 135 and 182
The least common multiple (LCM) of 135 and 182 is 24570.
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 135 and 182?
First, calculate the GCD of 135 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 182 = 0 remainder 135 |
| 2 | 182 ÷ 135 = 1 remainder 47 |
| 3 | 135 ÷ 47 = 2 remainder 41 |
| 4 | 47 ÷ 41 = 1 remainder 6 |
| 5 | 41 ÷ 6 = 6 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 13 | 1417 |
| 161 and 155 | 24955 |
| 186 and 123 | 7626 |
| 69 and 80 | 5520 |
| 94 and 177 | 16638 |