Least Common Multiple (LCM) of 53 and 173
The least common multiple (LCM) of 53 and 173 is 9169.
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 173?
First, calculate the GCD of 53 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 173 = 0 remainder 53 |
| 2 | 173 ÷ 53 = 3 remainder 14 |
| 3 | 53 ÷ 14 = 3 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 |
|---|---|
| 102 and 113 | 11526 |
| 81 and 52 | 4212 |
| 107 and 17 | 1819 |
| 170 and 79 | 13430 |
| 21 and 130 | 2730 |