Least Common Multiple (LCM) of 176 and 65
The least common multiple (LCM) of 176 and 65 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 176 and 65?
First, calculate the GCD of 176 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 65 = 2 remainder 46 |
| 2 | 65 ÷ 46 = 1 remainder 19 |
| 3 | 46 ÷ 19 = 2 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 25 | 2550 |
| 42 and 75 | 1050 |
| 41 and 67 | 2747 |
| 182 and 197 | 35854 |
| 107 and 136 | 14552 |