Least Common Multiple (LCM) of 174 and 112
The least common multiple (LCM) of 174 and 112 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 174 and 112?
First, calculate the GCD of 174 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 112 = 1 remainder 62 |
| 2 | 112 ÷ 62 = 1 remainder 50 |
| 3 | 62 ÷ 50 = 1 remainder 12 |
| 4 | 50 ÷ 12 = 4 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 190 | 13680 |
| 199 and 151 | 30049 |
| 149 and 107 | 15943 |
| 175 and 57 | 9975 |
| 117 and 99 | 1287 |