Least Common Multiple (LCM) of 145 and 197
The least common multiple (LCM) of 145 and 197 is 28565.
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 145 and 197?
First, calculate the GCD of 145 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 197 = 0 remainder 145 |
| 2 | 197 ÷ 145 = 1 remainder 52 |
| 3 | 145 ÷ 52 = 2 remainder 41 |
| 4 | 52 ÷ 41 = 1 remainder 11 |
| 5 | 41 ÷ 11 = 3 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 128 | 4992 |
| 196 and 74 | 7252 |
| 65 and 73 | 4745 |
| 91 and 17 | 1547 |
| 127 and 106 | 13462 |