Least Common Multiple (LCM) of 154 and 200
The least common multiple (LCM) of 154 and 200 is 15400.
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 200?
First, calculate the GCD of 154 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 200 = 0 remainder 154 |
| 2 | 200 ÷ 154 = 1 remainder 46 |
| 3 | 154 ÷ 46 = 3 remainder 16 |
| 4 | 46 ÷ 16 = 2 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 168 | 2856 |
| 132 and 122 | 8052 |
| 31 and 156 | 4836 |
| 42 and 11 | 462 |
| 85 and 158 | 13430 |