Least Common Multiple (LCM) of 65 and 176
The least common multiple (LCM) of 65 and 176 is 11440.
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 176?
First, calculate the GCD of 65 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 176 = 0 remainder 65 |
| 2 | 176 ÷ 65 = 2 remainder 46 |
| 3 | 65 ÷ 46 = 1 remainder 19 |
| 4 | 46 ÷ 19 = 2 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 39 | 4017 |
| 82 and 66 | 2706 |
| 15 and 23 | 345 |
| 135 and 159 | 7155 |
| 117 and 27 | 351 |