Least Common Multiple (LCM) of 53 and 198
The least common multiple (LCM) of 53 and 198 is 10494.
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 53 and 198?
First, calculate the GCD of 53 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 198 = 0 remainder 53 |
| 2 | 198 ÷ 53 = 3 remainder 39 |
| 3 | 53 ÷ 39 = 1 remainder 14 |
| 4 | 39 ÷ 14 = 2 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 11 | 1991 |
| 30 and 57 | 570 |
| 67 and 36 | 2412 |
| 134 and 14 | 938 |
| 175 and 134 | 23450 |