Least Common Multiple (LCM) of 112 and 158
The least common multiple (LCM) of 112 and 158 is 8848.
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 158?
First, calculate the GCD of 112 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 158 = 0 remainder 112 |
| 2 | 158 ÷ 112 = 1 remainder 46 |
| 3 | 112 ÷ 46 = 2 remainder 20 |
| 4 | 46 ÷ 20 = 2 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 81 | 9801 |
| 115 and 87 | 10005 |
| 14 and 115 | 1610 |
| 30 and 156 | 780 |
| 138 and 71 | 9798 |