Least Common Multiple (LCM) of 105 and 200
The least common multiple (LCM) of 105 and 200 is 4200.
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 105 and 200?
First, calculate the GCD of 105 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 200 = 0 remainder 105 |
| 2 | 200 ÷ 105 = 1 remainder 95 |
| 3 | 105 ÷ 95 = 1 remainder 10 |
| 4 | 95 ÷ 10 = 9 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 145 | 145 |
| 166 and 58 | 4814 |
| 21 and 21 | 21 |
| 26 and 121 | 3146 |
| 60 and 103 | 6180 |