Least Common Multiple (LCM) of 61 and 131
The least common multiple (LCM) of 61 and 131 is 7991.
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 61 and 131?
First, calculate the GCD of 61 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 131 = 0 remainder 61 |
| 2 | 131 ÷ 61 = 2 remainder 9 |
| 3 | 61 ÷ 9 = 6 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 41 | 2009 |
| 46 and 40 | 920 |
| 195 and 106 | 20670 |
| 199 and 141 | 28059 |
| 45 and 100 | 900 |