Least Common Multiple (LCM) of 100 and 131
The least common multiple (LCM) of 100 and 131 is 13100.
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 131?
First, calculate the GCD of 100 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 131 = 0 remainder 100 |
| 2 | 131 ÷ 100 = 1 remainder 31 |
| 3 | 100 ÷ 31 = 3 remainder 7 |
| 4 | 31 ÷ 7 = 4 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 25 | 725 |
| 197 and 197 | 197 |
| 45 and 171 | 855 |
| 189 and 183 | 11529 |
| 142 and 169 | 23998 |