Least Common Multiple (LCM) of 26 and 117
The least common multiple (LCM) of 26 and 117 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 26 and 117?
First, calculate the GCD of 26 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 117 = 0 remainder 26 |
| 2 | 117 ÷ 26 = 4 remainder 13 |
| 3 | 26 ÷ 13 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 200 | 7800 |
| 65 and 150 | 1950 |
| 30 and 10 | 30 |
| 130 and 96 | 6240 |
| 80 and 42 | 1680 |