Least Common Multiple (LCM) of 135 and 183
The least common multiple (LCM) of 135 and 183 is 8235.
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 183?
First, calculate the GCD of 135 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 183 = 0 remainder 135 |
| 2 | 183 ÷ 135 = 1 remainder 48 |
| 3 | 135 ÷ 48 = 2 remainder 39 |
| 4 | 48 ÷ 39 = 1 remainder 9 |
| 5 | 39 ÷ 9 = 4 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 77 | 13706 |
| 187 and 163 | 30481 |
| 118 and 59 | 118 |
| 196 and 25 | 4900 |
| 130 and 16 | 1040 |