Least Common Multiple (LCM) of 49 and 200
The least common multiple (LCM) of 49 and 200 is 9800.
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 49 and 200?
First, calculate the GCD of 49 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 200 = 0 remainder 49 |
| 2 | 200 ÷ 49 = 4 remainder 4 |
| 3 | 49 ÷ 4 = 12 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 194 | 14744 |
| 194 and 22 | 2134 |
| 87 and 185 | 16095 |
| 108 and 57 | 2052 |
| 200 and 87 | 17400 |