Least Common Multiple (LCM) of 26 and 119
The least common multiple (LCM) of 26 and 119 is 3094.
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 119?
First, calculate the GCD of 26 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 119 = 0 remainder 26 |
| 2 | 119 ÷ 26 = 4 remainder 15 |
| 3 | 26 ÷ 15 = 1 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 172 | 8772 |
| 57 and 27 | 513 |
| 109 and 100 | 10900 |
| 131 and 43 | 5633 |
| 60 and 115 | 1380 |