Least Common Multiple (LCM) of 200 and 78
The least common multiple (LCM) of 200 and 78 is 7800.
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 78?
First, calculate the GCD of 200 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 78 = 2 remainder 44 |
| 2 | 78 ÷ 44 = 1 remainder 34 |
| 3 | 44 ÷ 34 = 1 remainder 10 |
| 4 | 34 ÷ 10 = 3 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 116 | 18444 |
| 101 and 159 | 16059 |
| 136 and 118 | 8024 |
| 125 and 132 | 16500 |
| 65 and 33 | 2145 |