Least Common Multiple (LCM) of 112 and 175
The least common multiple (LCM) of 112 and 175 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 112 and 175?
First, calculate the GCD of 112 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 175 = 0 remainder 112 |
| 2 | 175 ÷ 112 = 1 remainder 63 |
| 3 | 112 ÷ 63 = 1 remainder 49 |
| 4 | 63 ÷ 49 = 1 remainder 14 |
| 5 | 49 ÷ 14 = 3 remainder 7 |
| 6 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 69 | 12144 |
| 145 and 32 | 4640 |
| 114 and 93 | 3534 |
| 165 and 121 | 1815 |
| 86 and 90 | 3870 |