Least Common Multiple (LCM) of 103 and 141
The least common multiple (LCM) of 103 and 141 is 14523.
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 141?
First, calculate the GCD of 103 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 141 = 0 remainder 103 |
| 2 | 141 ÷ 103 = 1 remainder 38 |
| 3 | 103 ÷ 38 = 2 remainder 27 |
| 4 | 38 ÷ 27 = 1 remainder 11 |
| 5 | 27 ÷ 11 = 2 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 150 | 1050 |
| 76 and 129 | 9804 |
| 183 and 145 | 26535 |
| 143 and 138 | 19734 |
| 199 and 198 | 39402 |