Least Common Multiple (LCM) of 102 and 56
The least common multiple (LCM) of 102 and 56 is 2856.
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 56?
First, calculate the GCD of 102 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 56 = 1 remainder 46 |
| 2 | 56 ÷ 46 = 1 remainder 10 |
| 3 | 46 ÷ 10 = 4 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 115 | 6555 |
| 29 and 177 | 5133 |
| 193 and 101 | 19493 |
| 48 and 43 | 2064 |
| 90 and 172 | 7740 |