Least Common Multiple (LCM) of 28 and 102
The least common multiple (LCM) of 28 and 102 is 1428.
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 102?
First, calculate the GCD of 28 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 102 = 0 remainder 28 |
| 2 | 102 ÷ 28 = 3 remainder 18 |
| 3 | 28 ÷ 18 = 1 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 53 | 2120 |
| 18 and 121 | 2178 |
| 10 and 144 | 720 |
| 146 and 72 | 5256 |
| 189 and 38 | 7182 |