Least Common Multiple (LCM) of 196 and 112
The least common multiple (LCM) of 196 and 112 is 784.
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 196 and 112?
First, calculate the GCD of 196 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 112 = 1 remainder 84 |
| 2 | 112 ÷ 84 = 1 remainder 28 |
| 3 | 84 ÷ 28 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 133 | 7182 |
| 34 and 134 | 2278 |
| 150 and 39 | 1950 |
| 121 and 134 | 16214 |
| 169 and 188 | 31772 |