Least Common Multiple (LCM) of 46 and 197
The least common multiple (LCM) of 46 and 197 is 9062.
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 46 and 197?
First, calculate the GCD of 46 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 197 = 0 remainder 46 |
| 2 | 197 ÷ 46 = 4 remainder 13 |
| 3 | 46 ÷ 13 = 3 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 36 | 144 |
| 82 and 195 | 15990 |
| 65 and 159 | 10335 |
| 180 and 119 | 21420 |
| 153 and 138 | 7038 |