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 |
|---|---|
| 180 and 179 | 32220 |
| 114 and 27 | 1026 |
| 67 and 65 | 4355 |
| 161 and 141 | 22701 |
| 151 and 117 | 17667 |