Least Common Multiple (LCM) of 86 and 169
The least common multiple (LCM) of 86 and 169 is 14534.
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 169?
First, calculate the GCD of 86 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 169 = 0 remainder 86 |
| 2 | 169 ÷ 86 = 1 remainder 83 |
| 3 | 86 ÷ 83 = 1 remainder 3 |
| 4 | 83 ÷ 3 = 27 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 109 | 15914 |
| 181 and 61 | 11041 |
| 36 and 144 | 144 |
| 12 and 145 | 1740 |
| 176 and 194 | 17072 |