Least Common Multiple (LCM) of 199 and 53
The least common multiple (LCM) of 199 and 53 is 10547.
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 53?
First, calculate the GCD of 199 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 53 = 3 remainder 40 |
| 2 | 53 ÷ 40 = 1 remainder 13 |
| 3 | 40 ÷ 13 = 3 remainder 1 |
| 4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 120 | 1080 |
| 72 and 138 | 1656 |
| 149 and 66 | 9834 |
| 187 and 166 | 31042 |
| 25 and 150 | 150 |