Least Common Multiple (LCM) of 198 and 53
The least common multiple (LCM) of 198 and 53 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 198 and 53?
First, calculate the GCD of 198 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 53 = 3 remainder 39 |
| 2 | 53 ÷ 39 = 1 remainder 14 |
| 3 | 39 ÷ 14 = 2 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 115 | 16445 |
| 151 and 116 | 17516 |
| 115 and 31 | 3565 |
| 34 and 66 | 1122 |
| 180 and 33 | 1980 |