Least Common Multiple (LCM) of 86 and 164
The least common multiple (LCM) of 86 and 164 is 7052.
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 164?
First, calculate the GCD of 86 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 164 = 0 remainder 86 |
| 2 | 164 ÷ 86 = 1 remainder 78 |
| 3 | 86 ÷ 78 = 1 remainder 8 |
| 4 | 78 ÷ 8 = 9 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 41 | 5084 |
| 165 and 59 | 9735 |
| 21 and 142 | 2982 |
| 35 and 19 | 665 |
| 129 and 42 | 1806 |