Least Common Multiple (LCM) of 86 and 116
The least common multiple (LCM) of 86 and 116 is 4988.
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 86 and 116?
First, calculate the GCD of 86 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 116 = 0 remainder 86 |
| 2 | 116 ÷ 86 = 1 remainder 30 |
| 3 | 86 ÷ 30 = 2 remainder 26 |
| 4 | 30 ÷ 26 = 1 remainder 4 |
| 5 | 26 ÷ 4 = 6 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 56 | 840 |
| 44 and 169 | 7436 |
| 28 and 109 | 3052 |
| 116 and 196 | 5684 |
| 117 and 146 | 17082 |