Least Common Multiple (LCM) of 13 and 18
The least common multiple (LCM) of 13 and 18 is 234.
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 18?
First, calculate the GCD of 13 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 18 = 0 remainder 13 |
| 2 | 18 ÷ 13 = 1 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 |
|---|---|
| 89 and 130 | 11570 |
| 86 and 18 | 774 |
| 164 and 161 | 26404 |
| 169 and 116 | 19604 |
| 117 and 98 | 11466 |