Least Common Multiple (LCM) of 102 and 28
The least common multiple (LCM) of 102 and 28 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 102 and 28?
First, calculate the GCD of 102 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 28 = 3 remainder 18 |
| 2 | 28 ÷ 18 = 1 remainder 10 |
| 3 | 18 ÷ 10 = 1 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 35 | 175 |
| 138 and 75 | 3450 |
| 68 and 10 | 340 |
| 132 and 42 | 924 |
| 172 and 143 | 24596 |