Least Common Multiple (LCM) of 135 and 184
The least common multiple (LCM) of 135 and 184 is 24840.
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 184?
First, calculate the GCD of 135 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 184 = 0 remainder 135 |
| 2 | 184 ÷ 135 = 1 remainder 49 |
| 3 | 135 ÷ 49 = 2 remainder 37 |
| 4 | 49 ÷ 37 = 1 remainder 12 |
| 5 | 37 ÷ 12 = 3 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 78 | 1560 |
| 192 and 183 | 11712 |
| 167 and 41 | 6847 |
| 125 and 11 | 1375 |
| 35 and 129 | 4515 |