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 |
|---|---|
| 71 and 56 | 3976 |
| 132 and 104 | 3432 |
| 124 and 91 | 11284 |
| 43 and 162 | 6966 |
| 115 and 64 | 7360 |