Least Common Multiple (LCM) of 112 and 141
The least common multiple (LCM) of 112 and 141 is 15792.
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 141?
First, calculate the GCD of 112 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 141 = 0 remainder 112 |
| 2 | 141 ÷ 112 = 1 remainder 29 |
| 3 | 112 ÷ 29 = 3 remainder 25 |
| 4 | 29 ÷ 25 = 1 remainder 4 |
| 5 | 25 ÷ 4 = 6 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 43 | 1935 |
| 133 and 108 | 14364 |
| 18 and 27 | 54 |
| 167 and 112 | 18704 |
| 32 and 50 | 800 |