Least Common Multiple (LCM) of 40 and 103
The least common multiple (LCM) of 40 and 103 is 4120.
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 40 and 103?
First, calculate the GCD of 40 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 103 = 0 remainder 40 |
| 2 | 103 ÷ 40 = 2 remainder 23 |
| 3 | 40 ÷ 23 = 1 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 150 | 8400 |
| 165 and 175 | 5775 |
| 171 and 114 | 342 |
| 49 and 11 | 539 |
| 164 and 180 | 7380 |