Least Common Multiple (LCM) of 63 and 82
The least common multiple (LCM) of 63 and 82 is 5166.
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 63 and 82?
First, calculate the GCD of 63 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 82 = 0 remainder 63 |
| 2 | 82 ÷ 63 = 1 remainder 19 |
| 3 | 63 ÷ 19 = 3 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 93 | 4185 |
| 32 and 167 | 5344 |
| 103 and 108 | 11124 |
| 69 and 188 | 12972 |
| 93 and 126 | 3906 |