Least Common Multiple (LCM) of 112 and 174
The least common multiple (LCM) of 112 and 174 is 9744.
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 174?
First, calculate the GCD of 112 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 174 = 0 remainder 112 |
| 2 | 174 ÷ 112 = 1 remainder 62 |
| 3 | 112 ÷ 62 = 1 remainder 50 |
| 4 | 62 ÷ 50 = 1 remainder 12 |
| 5 | 50 ÷ 12 = 4 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 61 | 6405 |
| 160 and 180 | 1440 |
| 181 and 141 | 25521 |
| 56 and 144 | 1008 |
| 11 and 54 | 594 |