Least Common Multiple (LCM) of 103 and 55
The least common multiple (LCM) of 103 and 55 is 5665.
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 55?
First, calculate the GCD of 103 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 55 = 1 remainder 48 |
| 2 | 55 ÷ 48 = 1 remainder 7 |
| 3 | 48 ÷ 7 = 6 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 138 | 18078 |
| 33 and 164 | 5412 |
| 20 and 143 | 2860 |
| 102 and 142 | 7242 |
| 114 and 57 | 114 |