Least Common Multiple (LCM) of 52 and 199
The least common multiple (LCM) of 52 and 199 is 10348.
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 52 and 199?
First, calculate the GCD of 52 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 199 = 0 remainder 52 |
| 2 | 199 ÷ 52 = 3 remainder 43 |
| 3 | 52 ÷ 43 = 1 remainder 9 |
| 4 | 43 ÷ 9 = 4 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 157 | 21823 |
| 38 and 69 | 2622 |
| 197 and 110 | 21670 |
| 112 and 38 | 2128 |
| 55 and 117 | 6435 |