Least Common Multiple (LCM) of 74 and 200
The least common multiple (LCM) of 74 and 200 is 7400.
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 74 and 200?
First, calculate the GCD of 74 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 200 = 0 remainder 74 |
| 2 | 200 ÷ 74 = 2 remainder 52 |
| 3 | 74 ÷ 52 = 1 remainder 22 |
| 4 | 52 ÷ 22 = 2 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 164 | 5084 |
| 96 and 38 | 1824 |
| 195 and 100 | 3900 |
| 50 and 50 | 50 |
| 172 and 160 | 6880 |