Least Common Multiple (LCM) of 100 and 26
The least common multiple (LCM) of 100 and 26 is 1300.
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 100 and 26?
First, calculate the GCD of 100 and 26 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 26 = 3 remainder 22 |
| 2 | 26 ÷ 22 = 1 remainder 4 |
| 3 | 22 ÷ 4 = 5 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 162 | 3726 |
| 176 and 12 | 528 |
| 191 and 97 | 18527 |
| 122 and 165 | 20130 |
| 130 and 91 | 910 |