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 |
|---|---|
| 131 and 114 | 14934 |
| 170 and 77 | 13090 |
| 198 and 26 | 2574 |
| 129 and 77 | 9933 |
| 195 and 33 | 2145 |