Least Common Multiple (LCM) of 26 and 99
The least common multiple (LCM) of 26 and 99 is 2574.
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 99?
First, calculate the GCD of 26 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 99 = 0 remainder 26 |
| 2 | 99 ÷ 26 = 3 remainder 21 |
| 3 | 26 ÷ 21 = 1 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 71 | 12922 |
| 188 and 133 | 25004 |
| 146 and 117 | 17082 |
| 160 and 144 | 1440 |
| 174 and 77 | 13398 |