Least Common Multiple (LCM) of 105 and 143
The least common multiple (LCM) of 105 and 143 is 15015.
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 105 and 143?
First, calculate the GCD of 105 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 143 = 0 remainder 105 |
| 2 | 143 ÷ 105 = 1 remainder 38 |
| 3 | 105 ÷ 38 = 2 remainder 29 |
| 4 | 38 ÷ 29 = 1 remainder 9 |
| 5 | 29 ÷ 9 = 3 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 13 | 1053 |
| 91 and 76 | 6916 |
| 10 and 154 | 770 |
| 118 and 78 | 4602 |
| 166 and 144 | 11952 |