Least Common Multiple (LCM) of 86 and 133
The least common multiple (LCM) of 86 and 133 is 11438.
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 133?
First, calculate the GCD of 86 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 133 = 0 remainder 86 |
| 2 | 133 ÷ 86 = 1 remainder 47 |
| 3 | 86 ÷ 47 = 1 remainder 39 |
| 4 | 47 ÷ 39 = 1 remainder 8 |
| 5 | 39 ÷ 8 = 4 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 112 | 1232 |
| 180 and 193 | 34740 |
| 88 and 199 | 17512 |
| 12 and 67 | 804 |
| 20 and 127 | 2540 |