Least Common Multiple (LCM) of 112 and 143
The least common multiple (LCM) of 112 and 143 is 16016.
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 112 and 143?
First, calculate the GCD of 112 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 143 = 0 remainder 112 |
| 2 | 143 ÷ 112 = 1 remainder 31 |
| 3 | 112 ÷ 31 = 3 remainder 19 |
| 4 | 31 ÷ 19 = 1 remainder 12 |
| 5 | 19 ÷ 12 = 1 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 86 | 11954 |
| 181 and 77 | 13937 |
| 75 and 107 | 8025 |
| 199 and 24 | 4776 |
| 82 and 106 | 4346 |