Least Common Multiple (LCM) of 45 and 131
The least common multiple (LCM) of 45 and 131 is 5895.
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 45 and 131?
First, calculate the GCD of 45 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 131 = 0 remainder 45 |
| 2 | 131 ÷ 45 = 2 remainder 41 |
| 3 | 45 ÷ 41 = 1 remainder 4 |
| 4 | 41 ÷ 4 = 10 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 180 | 900 |
| 51 and 59 | 3009 |
| 60 and 89 | 5340 |
| 168 and 163 | 27384 |
| 170 and 169 | 28730 |