Least Common Multiple (LCM) of 144 and 63
The least common multiple (LCM) of 144 and 63 is 1008.
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 144 and 63?
First, calculate the GCD of 144 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 63 = 2 remainder 18 |
| 2 | 63 ÷ 18 = 3 remainder 9 |
| 3 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 106 | 5936 |
| 92 and 108 | 2484 |
| 57 and 81 | 1539 |
| 194 and 60 | 5820 |
| 198 and 106 | 10494 |