Least Common Multiple (LCM) of 103 and 56
The least common multiple (LCM) of 103 and 56 is 5768.
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 103 and 56?
First, calculate the GCD of 103 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 56 = 1 remainder 47 |
| 2 | 56 ÷ 47 = 1 remainder 9 |
| 3 | 47 ÷ 9 = 5 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 10 | 870 |
| 150 and 71 | 10650 |
| 123 and 137 | 16851 |
| 94 and 159 | 14946 |
| 77 and 145 | 11165 |