Least Common Multiple (LCM) of 103 and 140
The least common multiple (LCM) of 103 and 140 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 103 and 140?
First, calculate the GCD of 103 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 140 = 0 remainder 103 |
| 2 | 140 ÷ 103 = 1 remainder 37 |
| 3 | 103 ÷ 37 = 2 remainder 29 |
| 4 | 37 ÷ 29 = 1 remainder 8 |
| 5 | 29 ÷ 8 = 3 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 59 | 9735 |
| 163 and 22 | 3586 |
| 39 and 84 | 1092 |
| 128 and 156 | 4992 |
| 54 and 186 | 1674 |