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 |
|---|---|
| 125 and 190 | 4750 |
| 188 and 21 | 3948 |
| 40 and 94 | 1880 |
| 157 and 188 | 29516 |
| 100 and 28 | 700 |