Least Common Multiple (LCM) of 65 and 161
The least common multiple (LCM) of 65 and 161 is 10465.
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 161?
First, calculate the GCD of 65 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 161 = 0 remainder 65 |
| 2 | 161 ÷ 65 = 2 remainder 31 |
| 3 | 65 ÷ 31 = 2 remainder 3 |
| 4 | 31 ÷ 3 = 10 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 67 | 7638 |
| 187 and 125 | 23375 |
| 39 and 167 | 6513 |
| 44 and 13 | 572 |
| 161 and 176 | 28336 |