Least Common Multiple (LCM) of 87 and 200
The least common multiple (LCM) of 87 and 200 is 17400.
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 87 and 200?
First, calculate the GCD of 87 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 200 = 0 remainder 87 |
| 2 | 200 ÷ 87 = 2 remainder 26 |
| 3 | 87 ÷ 26 = 3 remainder 9 |
| 4 | 26 ÷ 9 = 2 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 40 | 6120 |
| 109 and 42 | 4578 |
| 49 and 146 | 7154 |
| 14 and 30 | 210 |
| 28 and 130 | 1820 |