Least Common Multiple (LCM) of 56 and 102
The least common multiple (LCM) of 56 and 102 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 56 and 102?
First, calculate the GCD of 56 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 102 = 0 remainder 56 |
| 2 | 102 ÷ 56 = 1 remainder 46 |
| 3 | 56 ÷ 46 = 1 remainder 10 |
| 4 | 46 ÷ 10 = 4 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 164 | 15580 |
| 110 and 46 | 2530 |
| 162 and 179 | 28998 |
| 10 and 27 | 270 |
| 159 and 130 | 20670 |