Least Common Multiple (LCM) of 200 and 87
The least common multiple (LCM) of 200 and 87 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 200 and 87?
First, calculate the GCD of 200 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 87 = 2 remainder 26 |
| 2 | 87 ÷ 26 = 3 remainder 9 |
| 3 | 26 ÷ 9 = 2 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 79 | 10902 |
| 24 and 35 | 840 |
| 158 and 105 | 16590 |
| 159 and 116 | 18444 |
| 164 and 14 | 1148 |