Least Common Multiple (LCM) of 135 and 104
The least common multiple (LCM) of 135 and 104 is 14040.
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 104?
First, calculate the GCD of 135 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 104 = 1 remainder 31 |
| 2 | 104 ÷ 31 = 3 remainder 11 |
| 3 | 31 ÷ 11 = 2 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 38 | 1482 |
| 200 and 15 | 600 |
| 135 and 131 | 17685 |
| 102 and 16 | 816 |
| 102 and 105 | 3570 |