Least Common Multiple (LCM) of 48 and 199
The least common multiple (LCM) of 48 and 199 is 9552.
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 48 and 199?
First, calculate the GCD of 48 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 199 = 0 remainder 48 |
| 2 | 199 ÷ 48 = 4 remainder 7 |
| 3 | 48 ÷ 7 = 6 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 104 | 10712 |
| 188 and 166 | 15604 |
| 64 and 176 | 704 |
| 99 and 153 | 1683 |
| 109 and 172 | 18748 |