Least Common Multiple (LCM) of 17 and 63
The least common multiple (LCM) of 17 and 63 is 1071.
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 17 and 63?
First, calculate the GCD of 17 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 63 = 0 remainder 17 |
| 2 | 63 ÷ 17 = 3 remainder 12 |
| 3 | 17 ÷ 12 = 1 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 95 | 3420 |
| 181 and 40 | 7240 |
| 11 and 92 | 1012 |
| 105 and 127 | 13335 |
| 61 and 21 | 1281 |