Least Common Multiple (LCM) of 112 and 176
The least common multiple (LCM) of 112 and 176 is 1232.
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 176?
First, calculate the GCD of 112 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 176 = 0 remainder 112 |
| 2 | 176 ÷ 112 = 1 remainder 64 |
| 3 | 112 ÷ 64 = 1 remainder 48 |
| 4 | 64 ÷ 48 = 1 remainder 16 |
| 5 | 48 ÷ 16 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 168 | 3864 |
| 133 and 120 | 15960 |
| 198 and 109 | 21582 |
| 38 and 74 | 1406 |
| 155 and 149 | 23095 |