Least Common Multiple (LCM) of 13 and 135
The least common multiple (LCM) of 13 and 135 is 1755.
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 13 and 135?
First, calculate the GCD of 13 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 135 = 0 remainder 13 |
| 2 | 135 ÷ 13 = 10 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 26 | 754 |
| 88 and 31 | 2728 |
| 94 and 17 | 1598 |
| 109 and 193 | 21037 |
| 136 and 16 | 272 |