Least Common Multiple (LCM) of 112 and 173
The least common multiple (LCM) of 112 and 173 is 19376.
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 173?
First, calculate the GCD of 112 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 173 = 0 remainder 112 |
| 2 | 173 ÷ 112 = 1 remainder 61 |
| 3 | 112 ÷ 61 = 1 remainder 51 |
| 4 | 61 ÷ 51 = 1 remainder 10 |
| 5 | 51 ÷ 10 = 5 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 161 | 3381 |
| 187 and 88 | 1496 |
| 160 and 165 | 5280 |
| 113 and 170 | 19210 |
| 193 and 185 | 35705 |