Least Common Multiple (LCM) of 116 and 178
The least common multiple (LCM) of 116 and 178 is 10324.
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 116 and 178?
First, calculate the GCD of 116 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 178 = 0 remainder 116 |
| 2 | 178 ÷ 116 = 1 remainder 62 |
| 3 | 116 ÷ 62 = 1 remainder 54 |
| 4 | 62 ÷ 54 = 1 remainder 8 |
| 5 | 54 ÷ 8 = 6 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 149 | 18178 |
| 40 and 145 | 1160 |
| 58 and 48 | 1392 |
| 76 and 63 | 4788 |
| 186 and 95 | 17670 |