Least Common Multiple (LCM) of 177 and 108
The least common multiple (LCM) of 177 and 108 is 6372.
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 177 and 108?
First, calculate the GCD of 177 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 108 = 1 remainder 69 |
| 2 | 108 ÷ 69 = 1 remainder 39 |
| 3 | 69 ÷ 39 = 1 remainder 30 |
| 4 | 39 ÷ 30 = 1 remainder 9 |
| 5 | 30 ÷ 9 = 3 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 156 | 14820 |
| 16 and 109 | 1744 |
| 47 and 59 | 2773 |
| 198 and 58 | 5742 |
| 41 and 75 | 3075 |