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 |
|---|---|
| 165 and 150 | 1650 |
| 61 and 27 | 1647 |
| 200 and 104 | 2600 |
| 70 and 110 | 770 |
| 64 and 55 | 3520 |