Least Common Multiple (LCM) of 112 and 177
The least common multiple (LCM) of 112 and 177 is 19824.
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 112 and 177?
First, calculate the GCD of 112 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 177 = 0 remainder 112 |
| 2 | 177 ÷ 112 = 1 remainder 65 |
| 3 | 112 ÷ 65 = 1 remainder 47 |
| 4 | 65 ÷ 47 = 1 remainder 18 |
| 5 | 47 ÷ 18 = 2 remainder 11 |
| 6 | 18 ÷ 11 = 1 remainder 7 |
| 7 | 11 ÷ 7 = 1 remainder 4 |
| 8 | 7 ÷ 4 = 1 remainder 3 |
| 9 | 4 ÷ 3 = 1 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 183 | 20496 |
| 30 and 171 | 1710 |
| 129 and 87 | 3741 |
| 51 and 104 | 5304 |
| 77 and 165 | 1155 |