Least Common Multiple (LCM) of 86 and 132
The least common multiple (LCM) of 86 and 132 is 5676.
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 132?
First, calculate the GCD of 86 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 132 = 0 remainder 86 |
| 2 | 132 ÷ 86 = 1 remainder 46 |
| 3 | 86 ÷ 46 = 1 remainder 40 |
| 4 | 46 ÷ 40 = 1 remainder 6 |
| 5 | 40 ÷ 6 = 6 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 129 | 10320 |
| 144 and 178 | 12816 |
| 104 and 60 | 1560 |
| 184 and 78 | 7176 |
| 157 and 54 | 8478 |