Least Common Multiple (LCM) of 83 and 112
The least common multiple (LCM) of 83 and 112 is 9296.
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 83 and 112?
First, calculate the GCD of 83 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 112 = 0 remainder 83 |
| 2 | 112 ÷ 83 = 1 remainder 29 |
| 3 | 83 ÷ 29 = 2 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 |
|---|---|
| 137 and 184 | 25208 |
| 13 and 133 | 1729 |
| 128 and 171 | 21888 |
| 73 and 104 | 7592 |
| 145 and 108 | 15660 |