Least Common Multiple (LCM) of 47 and 63
The least common multiple (LCM) of 47 and 63 is 2961.
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 47 and 63?
First, calculate the GCD of 47 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 63 = 0 remainder 47 |
| 2 | 63 ÷ 47 = 1 remainder 16 |
| 3 | 47 ÷ 16 = 2 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 17 | 255 |
| 78 and 56 | 2184 |
| 136 and 105 | 14280 |
| 79 and 111 | 8769 |
| 183 and 108 | 6588 |