Least Common Multiple (LCM) of 86 and 145
The least common multiple (LCM) of 86 and 145 is 12470.
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 145?
First, calculate the GCD of 86 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 145 = 0 remainder 86 |
| 2 | 145 ÷ 86 = 1 remainder 59 |
| 3 | 86 ÷ 59 = 1 remainder 27 |
| 4 | 59 ÷ 27 = 2 remainder 5 |
| 5 | 27 ÷ 5 = 5 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 29 | 4002 |
| 65 and 192 | 12480 |
| 105 and 134 | 14070 |
| 48 and 116 | 1392 |
| 65 and 155 | 2015 |