Least Common Multiple (LCM) of 178 and 197
The least common multiple (LCM) of 178 and 197 is 35066.
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 178 and 197?
First, calculate the GCD of 178 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 197 = 0 remainder 178 |
| 2 | 197 ÷ 178 = 1 remainder 19 |
| 3 | 178 ÷ 19 = 9 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 190 | 14630 |
| 120 and 85 | 2040 |
| 144 and 159 | 7632 |
| 29 and 97 | 2813 |
| 123 and 178 | 21894 |