Least Common Multiple (LCM) of 53 and 200
The least common multiple (LCM) of 53 and 200 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 53 and 200?
First, calculate the GCD of 53 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 200 = 0 remainder 53 |
| 2 | 200 ÷ 53 = 3 remainder 41 |
| 3 | 53 ÷ 41 = 1 remainder 12 |
| 4 | 41 ÷ 12 = 3 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 48 | 816 |
| 180 and 40 | 360 |
| 40 and 119 | 4760 |
| 13 and 167 | 2171 |
| 78 and 45 | 1170 |