Least Common Multiple (LCM) of 154 and 199
The least common multiple (LCM) of 154 and 199 is 30646.
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 199?
First, calculate the GCD of 154 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 199 = 0 remainder 154 |
| 2 | 199 ÷ 154 = 1 remainder 45 |
| 3 | 154 ÷ 45 = 3 remainder 19 |
| 4 | 45 ÷ 19 = 2 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 198 | 5742 |
| 142 and 144 | 10224 |
| 96 and 130 | 6240 |
| 185 and 102 | 18870 |
| 135 and 75 | 675 |