Least Common Multiple (LCM) of 118 and 103
The least common multiple (LCM) of 118 and 103 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 118 and 103?
First, calculate the GCD of 118 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 103 = 1 remainder 15 |
| 2 | 103 ÷ 15 = 6 remainder 13 |
| 3 | 15 ÷ 13 = 1 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 35 | 140 |
| 106 and 176 | 9328 |
| 157 and 91 | 14287 |
| 52 and 118 | 3068 |
| 155 and 36 | 5580 |