Least Common Multiple (LCM) of 15 and 26
The least common multiple (LCM) of 15 and 26 is 390.
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 15 and 26?
First, calculate the GCD of 15 and 26 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 26 = 0 remainder 15 |
| 2 | 26 ÷ 15 = 1 remainder 11 |
| 3 | 15 ÷ 11 = 1 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 164 | 164 |
| 14 and 67 | 938 |
| 175 and 19 | 3325 |
| 53 and 182 | 9646 |
| 10 and 81 | 810 |