Least Common Multiple (LCM) of 199 and 48
The least common multiple (LCM) of 199 and 48 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 199 and 48?
First, calculate the GCD of 199 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 48 = 4 remainder 7 |
| 2 | 48 ÷ 7 = 6 remainder 6 |
| 3 | 7 ÷ 6 = 1 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 33 | 132 |
| 60 and 117 | 2340 |
| 133 and 102 | 13566 |
| 161 and 115 | 805 |
| 144 and 73 | 10512 |