Least Common Multiple (LCM) of 104 and 135
The least common multiple (LCM) of 104 and 135 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 104 and 135?
First, calculate the GCD of 104 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 135 = 0 remainder 104 |
| 2 | 135 ÷ 104 = 1 remainder 31 |
| 3 | 104 ÷ 31 = 3 remainder 11 |
| 4 | 31 ÷ 11 = 2 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 105 | 15960 |
| 132 and 157 | 20724 |
| 47 and 188 | 188 |
| 196 and 51 | 9996 |
| 45 and 193 | 8685 |