Least Common Multiple (LCM) of 116 and 170
The least common multiple (LCM) of 116 and 170 is 9860.
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 170?
First, calculate the GCD of 116 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 170 = 0 remainder 116 |
| 2 | 170 ÷ 116 = 1 remainder 54 |
| 3 | 116 ÷ 54 = 2 remainder 8 |
| 4 | 54 ÷ 8 = 6 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 198 | 4950 |
| 58 and 82 | 2378 |
| 78 and 82 | 3198 |
| 170 and 149 | 25330 |
| 95 and 160 | 3040 |