Least Common Multiple (LCM) of 63 and 143
The least common multiple (LCM) of 63 and 143 is 9009.
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 143?
First, calculate the GCD of 63 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 143 = 0 remainder 63 |
| 2 | 143 ÷ 63 = 2 remainder 17 |
| 3 | 63 ÷ 17 = 3 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 31 | 2604 |
| 21 and 197 | 4137 |
| 48 and 200 | 1200 |
| 39 and 154 | 6006 |
| 29 and 100 | 2900 |