Least Common Multiple (LCM) of 51 and 200
The least common multiple (LCM) of 51 and 200 is 10200.
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 51 and 200?
First, calculate the GCD of 51 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 200 = 0 remainder 51 |
| 2 | 200 ÷ 51 = 3 remainder 47 |
| 3 | 51 ÷ 47 = 1 remainder 4 |
| 4 | 47 ÷ 4 = 11 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 73 | 10366 |
| 83 and 118 | 9794 |
| 100 and 120 | 600 |
| 124 and 82 | 5084 |
| 142 and 96 | 6816 |