Least Common Multiple (LCM) of 26 and 126
The least common multiple (LCM) of 26 and 126 is 1638.
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 26 and 126?
First, calculate the GCD of 26 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 126 = 0 remainder 26 |
| 2 | 126 ÷ 26 = 4 remainder 22 |
| 3 | 26 ÷ 22 = 1 remainder 4 |
| 4 | 22 ÷ 4 = 5 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 143 | 21736 |
| 169 and 26 | 338 |
| 25 and 123 | 3075 |
| 173 and 36 | 6228 |
| 50 and 189 | 9450 |