Least Common Multiple (LCM) of 86 and 105
The least common multiple (LCM) of 86 and 105 is 9030.
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 105?
First, calculate the GCD of 86 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 105 = 0 remainder 86 |
| 2 | 105 ÷ 86 = 1 remainder 19 |
| 3 | 86 ÷ 19 = 4 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 20 | 580 |
| 192 and 50 | 4800 |
| 60 and 63 | 1260 |
| 29 and 68 | 1972 |
| 151 and 150 | 22650 |