Least Common Multiple (LCM) of 178 and 112
The least common multiple (LCM) of 178 and 112 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 178 and 112?
First, calculate the GCD of 178 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 112 = 1 remainder 66 |
| 2 | 112 ÷ 66 = 1 remainder 46 |
| 3 | 66 ÷ 46 = 1 remainder 20 |
| 4 | 46 ÷ 20 = 2 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 54 | 7398 |
| 141 and 81 | 3807 |
| 158 and 150 | 11850 |
| 99 and 159 | 5247 |
| 133 and 194 | 25802 |