Least Common Multiple (LCM) of 200 and 53
The least common multiple (LCM) of 200 and 53 is 10600.
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 200 and 53?
First, calculate the GCD of 200 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 53 = 3 remainder 41 |
| 2 | 53 ÷ 41 = 1 remainder 12 |
| 3 | 41 ÷ 12 = 3 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 34 | 442 |
| 137 and 54 | 7398 |
| 163 and 125 | 20375 |
| 28 and 25 | 700 |
| 151 and 156 | 23556 |