Least Common Multiple (LCM) of 28 and 144
The least common multiple (LCM) of 28 and 144 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 28 and 144?
First, calculate the GCD of 28 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 144 = 0 remainder 28 |
| 2 | 144 ÷ 28 = 5 remainder 4 |
| 3 | 28 ÷ 4 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 138 | 2346 |
| 82 and 119 | 9758 |
| 142 and 100 | 7100 |
| 174 and 133 | 23142 |
| 129 and 45 | 1935 |