Least Common Multiple (LCM) of 140 and 103
The least common multiple (LCM) of 140 and 103 is 14420.
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 140 and 103?
First, calculate the GCD of 140 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 103 = 1 remainder 37 |
| 2 | 103 ÷ 37 = 2 remainder 29 |
| 3 | 37 ÷ 29 = 1 remainder 8 |
| 4 | 29 ÷ 8 = 3 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 142 | 21158 |
| 199 and 11 | 2189 |
| 81 and 115 | 9315 |
| 135 and 98 | 13230 |
| 174 and 190 | 16530 |