Least Common Multiple (LCM) of 112 and 170
The least common multiple (LCM) of 112 and 170 is 9520.
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 170?
First, calculate the GCD of 112 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 170 = 0 remainder 112 |
| 2 | 170 ÷ 112 = 1 remainder 58 |
| 3 | 112 ÷ 58 = 1 remainder 54 |
| 4 | 58 ÷ 54 = 1 remainder 4 |
| 5 | 54 ÷ 4 = 13 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 187 | 12903 |
| 196 and 49 | 196 |
| 125 and 40 | 1000 |
| 100 and 195 | 3900 |
| 78 and 33 | 858 |