Least Common Multiple (LCM) of 63 and 83
The least common multiple (LCM) of 63 and 83 is 5229.
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 83?
First, calculate the GCD of 63 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 83 = 0 remainder 63 |
| 2 | 83 ÷ 63 = 1 remainder 20 |
| 3 | 63 ÷ 20 = 3 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 114 | 3306 |
| 183 and 164 | 30012 |
| 103 and 85 | 8755 |
| 68 and 48 | 816 |
| 191 and 126 | 24066 |