Least Common Multiple (LCM) of 116 and 176
The least common multiple (LCM) of 116 and 176 is 5104.
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 176?
First, calculate the GCD of 116 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 176 = 0 remainder 116 |
| 2 | 176 ÷ 116 = 1 remainder 60 |
| 3 | 116 ÷ 60 = 1 remainder 56 |
| 4 | 60 ÷ 56 = 1 remainder 4 |
| 5 | 56 ÷ 4 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 43 | 7138 |
| 131 and 37 | 4847 |
| 96 and 77 | 7392 |
| 71 and 172 | 12212 |
| 16 and 136 | 272 |