Least Common Multiple (LCM) of 117 and 103
The least common multiple (LCM) of 117 and 103 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 117 and 103?
First, calculate the GCD of 117 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 103 = 1 remainder 14 |
| 2 | 103 ÷ 14 = 7 remainder 5 |
| 3 | 14 ÷ 5 = 2 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 150 | 750 |
| 110 and 108 | 5940 |
| 139 and 159 | 22101 |
| 116 and 103 | 11948 |
| 153 and 177 | 9027 |