Least Common Multiple (LCM) of 193 and 53
The least common multiple (LCM) of 193 and 53 is 10229.
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 193 and 53?
First, calculate the GCD of 193 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 53 = 3 remainder 34 |
| 2 | 53 ÷ 34 = 1 remainder 19 |
| 3 | 34 ÷ 19 = 1 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 40 | 1080 |
| 107 and 95 | 10165 |
| 132 and 77 | 924 |
| 171 and 37 | 6327 |
| 66 and 59 | 3894 |