Least Common Multiple (LCM) of 116 and 142
The least common multiple (LCM) of 116 and 142 is 8236.
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 142?
First, calculate the GCD of 116 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 142 = 0 remainder 116 |
| 2 | 142 ÷ 116 = 1 remainder 26 |
| 3 | 116 ÷ 26 = 4 remainder 12 |
| 4 | 26 ÷ 12 = 2 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 17 | 2652 |
| 189 and 16 | 3024 |
| 109 and 158 | 17222 |
| 84 and 55 | 4620 |
| 30 and 161 | 4830 |