Least Common Multiple (LCM) of 112 and 171
The least common multiple (LCM) of 112 and 171 is 19152.
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 171?
First, calculate the GCD of 112 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 171 = 0 remainder 112 |
| 2 | 171 ÷ 112 = 1 remainder 59 |
| 3 | 112 ÷ 59 = 1 remainder 53 |
| 4 | 59 ÷ 53 = 1 remainder 6 |
| 5 | 53 ÷ 6 = 8 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 67 | 13266 |
| 123 and 187 | 23001 |
| 194 and 92 | 8924 |
| 91 and 198 | 18018 |
| 168 and 47 | 7896 |