Least Common Multiple (LCM) of 82 and 147
The least common multiple (LCM) of 82 and 147 is 12054.
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 82 and 147?
First, calculate the GCD of 82 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 147 = 0 remainder 82 |
| 2 | 147 ÷ 82 = 1 remainder 65 |
| 3 | 82 ÷ 65 = 1 remainder 17 |
| 4 | 65 ÷ 17 = 3 remainder 14 |
| 5 | 17 ÷ 14 = 1 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 101 | 6262 |
| 22 and 84 | 924 |
| 32 and 14 | 224 |
| 114 and 72 | 1368 |
| 18 and 103 | 1854 |