Least Common Multiple (LCM) of 13 and 138
The least common multiple (LCM) of 13 and 138 is 1794.
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 138?
First, calculate the GCD of 13 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 138 = 0 remainder 13 |
| 2 | 138 ÷ 13 = 10 remainder 8 |
| 3 | 13 ÷ 8 = 1 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 113 | 18645 |
| 184 and 164 | 7544 |
| 33 and 30 | 330 |
| 116 and 117 | 13572 |
| 106 and 79 | 8374 |