Least Common Multiple (LCM) of 46 and 103
The least common multiple (LCM) of 46 and 103 is 4738.
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 46 and 103?
First, calculate the GCD of 46 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 103 = 0 remainder 46 |
| 2 | 103 ÷ 46 = 2 remainder 11 |
| 3 | 46 ÷ 11 = 4 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 103 | 13905 |
| 126 and 98 | 882 |
| 77 and 72 | 5544 |
| 19 and 20 | 380 |
| 186 and 81 | 5022 |