Least Common Multiple (LCM) of 112 and 196
The least common multiple (LCM) of 112 and 196 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 112 and 196?
First, calculate the GCD of 112 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 196 = 0 remainder 112 |
| 2 | 196 ÷ 112 = 1 remainder 84 |
| 3 | 112 ÷ 84 = 1 remainder 28 |
| 4 | 84 ÷ 28 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 106 | 11130 |
| 36 and 43 | 1548 |
| 151 and 95 | 14345 |
| 58 and 53 | 3074 |
| 61 and 68 | 4148 |