Least Common Multiple (LCM) of 177 and 96
The least common multiple (LCM) of 177 and 96 is 5664.
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 96?
First, calculate the GCD of 177 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 96 = 1 remainder 81 |
| 2 | 96 ÷ 81 = 1 remainder 15 |
| 3 | 81 ÷ 15 = 5 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 177 | 24249 |
| 140 and 189 | 3780 |
| 136 and 182 | 12376 |
| 193 and 114 | 22002 |
| 45 and 56 | 2520 |