Least Common Multiple (LCM) of 10 and 26
The least common multiple (LCM) of 10 and 26 is 130.
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 10 and 26?
First, calculate the GCD of 10 and 26 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 26 = 0 remainder 10 |
| 2 | 26 ÷ 10 = 2 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 55 | 660 |
| 74 and 154 | 5698 |
| 41 and 165 | 6765 |
| 154 and 134 | 10318 |
| 12 and 64 | 192 |