Least Common Multiple (LCM) of 112 and 178
The least common multiple (LCM) of 112 and 178 is 9968.
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 178?
First, calculate the GCD of 112 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 178 = 0 remainder 112 |
| 2 | 178 ÷ 112 = 1 remainder 66 |
| 3 | 112 ÷ 66 = 1 remainder 46 |
| 4 | 66 ÷ 46 = 1 remainder 20 |
| 5 | 46 ÷ 20 = 2 remainder 6 |
| 6 | 20 ÷ 6 = 3 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 165 | 23430 |
| 198 and 183 | 12078 |
| 111 and 44 | 4884 |
| 110 and 115 | 2530 |
| 103 and 128 | 13184 |