Least Common Multiple (LCM) of 163 and 63
The least common multiple (LCM) of 163 and 63 is 10269.
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 163 and 63?
First, calculate the GCD of 163 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 63 = 2 remainder 37 |
| 2 | 63 ÷ 37 = 1 remainder 26 |
| 3 | 37 ÷ 26 = 1 remainder 11 |
| 4 | 26 ÷ 11 = 2 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 123 | 2091 |
| 20 and 112 | 560 |
| 154 and 46 | 3542 |
| 158 and 117 | 18486 |
| 14 and 30 | 210 |