Least Common Multiple (LCM) of 86 and 147
The least common multiple (LCM) of 86 and 147 is 12642.
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 147?
First, calculate the GCD of 86 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 147 = 0 remainder 86 |
| 2 | 147 ÷ 86 = 1 remainder 61 |
| 3 | 86 ÷ 61 = 1 remainder 25 |
| 4 | 61 ÷ 25 = 2 remainder 11 |
| 5 | 25 ÷ 11 = 2 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 112 | 5040 |
| 170 and 157 | 26690 |
| 47 and 134 | 6298 |
| 90 and 104 | 4680 |
| 78 and 24 | 312 |