Least Common Multiple (LCM) of 65 and 177
The least common multiple (LCM) of 65 and 177 is 11505.
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 177?
First, calculate the GCD of 65 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 177 = 0 remainder 65 |
| 2 | 177 ÷ 65 = 2 remainder 47 |
| 3 | 65 ÷ 47 = 1 remainder 18 |
| 4 | 47 ÷ 18 = 2 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 69 | 10833 |
| 170 and 154 | 13090 |
| 146 and 143 | 20878 |
| 21 and 167 | 3507 |
| 183 and 137 | 25071 |