Least Common Multiple (LCM) of 65 and 181
The least common multiple (LCM) of 65 and 181 is 11765.
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 65 and 181?
First, calculate the GCD of 65 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 181 = 0 remainder 65 |
| 2 | 181 ÷ 65 = 2 remainder 51 |
| 3 | 65 ÷ 51 = 1 remainder 14 |
| 4 | 51 ÷ 14 = 3 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 10 | 240 |
| 21 and 66 | 462 |
| 115 and 111 | 12765 |
| 125 and 61 | 7625 |
| 66 and 73 | 4818 |