Least Common Multiple (LCM) of 13 and 65
The least common multiple (LCM) of 13 and 65 is 65.
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 65?
First, calculate the GCD of 13 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 65 = 0 remainder 13 |
| 2 | 65 ÷ 13 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 164 | 3116 |
| 23 and 68 | 1564 |
| 89 and 168 | 14952 |
| 108 and 159 | 5724 |
| 161 and 117 | 18837 |