Least Common Multiple (LCM) of 154 and 197
The least common multiple (LCM) of 154 and 197 is 30338.
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 154 and 197?
First, calculate the GCD of 154 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 197 = 0 remainder 154 |
| 2 | 197 ÷ 154 = 1 remainder 43 |
| 3 | 154 ÷ 43 = 3 remainder 25 |
| 4 | 43 ÷ 25 = 1 remainder 18 |
| 5 | 25 ÷ 18 = 1 remainder 7 |
| 6 | 18 ÷ 7 = 2 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 119 | 17374 |
| 84 and 183 | 5124 |
| 51 and 102 | 102 |
| 87 and 112 | 9744 |
| 173 and 68 | 11764 |