Least Common Multiple (LCM) of 112 and 154
The least common multiple (LCM) of 112 and 154 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 154?
First, calculate the GCD of 112 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 154 = 0 remainder 112 |
| 2 | 154 ÷ 112 = 1 remainder 42 |
| 3 | 112 ÷ 42 = 2 remainder 28 |
| 4 | 42 ÷ 28 = 1 remainder 14 |
| 5 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 182 | 16744 |
| 19 and 166 | 3154 |
| 194 and 128 | 12416 |
| 114 and 167 | 19038 |
| 28 and 144 | 1008 |