Least Common Multiple (LCM) of 171 and 112
The least common multiple (LCM) of 171 and 112 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 171 and 112?
First, calculate the GCD of 171 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 112 = 1 remainder 59 |
| 2 | 112 ÷ 59 = 1 remainder 53 |
| 3 | 59 ÷ 53 = 1 remainder 6 |
| 4 | 53 ÷ 6 = 8 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 75 | 900 |
| 159 and 126 | 6678 |
| 130 and 138 | 8970 |
| 111 and 28 | 3108 |
| 53 and 46 | 2438 |