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 |
|---|---|
| 180 and 22 | 1980 |
| 136 and 129 | 17544 |
| 178 and 120 | 10680 |
| 42 and 161 | 966 |
| 57 and 176 | 10032 |