Least Common Multiple (LCM) of 111 and 178
The least common multiple (LCM) of 111 and 178 is 19758.
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 111 and 178?
First, calculate the GCD of 111 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 178 = 0 remainder 111 |
| 2 | 178 ÷ 111 = 1 remainder 67 |
| 3 | 111 ÷ 67 = 1 remainder 44 |
| 4 | 67 ÷ 44 = 1 remainder 23 |
| 5 | 44 ÷ 23 = 1 remainder 21 |
| 6 | 23 ÷ 21 = 1 remainder 2 |
| 7 | 21 ÷ 2 = 10 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 103 | 19261 |
| 184 and 119 | 21896 |
| 89 and 99 | 8811 |
| 159 and 124 | 19716 |
| 131 and 28 | 3668 |