Least Common Multiple (LCM) of 103 and 118
The least common multiple (LCM) of 103 and 118 is 12154.
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 118?
First, calculate the GCD of 103 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 118 = 0 remainder 103 |
| 2 | 118 ÷ 103 = 1 remainder 15 |
| 3 | 103 ÷ 15 = 6 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 31 | 465 |
| 137 and 54 | 7398 |
| 36 and 122 | 2196 |
| 121 and 56 | 6776 |
| 144 and 71 | 10224 |