Least Common Multiple (LCM) of 26 and 101
The least common multiple (LCM) of 26 and 101 is 2626.
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 101?
First, calculate the GCD of 26 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 101 = 0 remainder 26 |
| 2 | 101 ÷ 26 = 3 remainder 23 |
| 3 | 26 ÷ 23 = 1 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 111 | 1887 |
| 116 and 165 | 19140 |
| 54 and 77 | 4158 |
| 165 and 112 | 18480 |
| 178 and 142 | 12638 |