Least Common Multiple (LCM) of 112 and 197
The least common multiple (LCM) of 112 and 197 is 22064.
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 197?
First, calculate the GCD of 112 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 197 = 0 remainder 112 |
| 2 | 197 ÷ 112 = 1 remainder 85 |
| 3 | 112 ÷ 85 = 1 remainder 27 |
| 4 | 85 ÷ 27 = 3 remainder 4 |
| 5 | 27 ÷ 4 = 6 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 69 | 3657 |
| 39 and 63 | 819 |
| 123 and 185 | 22755 |
| 69 and 100 | 6900 |
| 145 and 98 | 14210 |