Least Common Multiple (LCM) of 175 and 112
The least common multiple (LCM) of 175 and 112 is 2800.
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 175 and 112?
First, calculate the GCD of 175 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 112 = 1 remainder 63 |
| 2 | 112 ÷ 63 = 1 remainder 49 |
| 3 | 63 ÷ 49 = 1 remainder 14 |
| 4 | 49 ÷ 14 = 3 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 129 | 24252 |
| 107 and 42 | 4494 |
| 31 and 198 | 6138 |
| 48 and 163 | 7824 |
| 87 and 74 | 6438 |