Least Common Multiple (LCM) of 103 and 117
The least common multiple (LCM) of 103 and 117 is 12051.
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 117?
First, calculate the GCD of 103 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 117 = 0 remainder 103 |
| 2 | 117 ÷ 103 = 1 remainder 14 |
| 3 | 103 ÷ 14 = 7 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 130 | 130 |
| 129 and 97 | 12513 |
| 44 and 41 | 1804 |
| 63 and 56 | 504 |
| 93 and 34 | 3162 |