Least Common Multiple (LCM) of 103 and 54
The least common multiple (LCM) of 103 and 54 is 5562.
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 54?
First, calculate the GCD of 103 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 54 = 1 remainder 49 |
| 2 | 54 ÷ 49 = 1 remainder 5 |
| 3 | 49 ÷ 5 = 9 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 58 | 2610 |
| 105 and 115 | 2415 |
| 132 and 75 | 3300 |
| 76 and 156 | 2964 |
| 108 and 123 | 4428 |