Least Common Multiple (LCM) of 65 and 173
The least common multiple (LCM) of 65 and 173 is 11245.
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 173?
First, calculate the GCD of 65 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 173 = 0 remainder 65 |
| 2 | 173 ÷ 65 = 2 remainder 43 |
| 3 | 65 ÷ 43 = 1 remainder 22 |
| 4 | 43 ÷ 22 = 1 remainder 21 |
| 5 | 22 ÷ 21 = 1 remainder 1 |
| 6 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 126 | 15246 |
| 110 and 116 | 6380 |
| 34 and 190 | 3230 |
| 142 and 168 | 11928 |
| 112 and 164 | 4592 |