Least Common Multiple (LCM) of 173 and 113
The least common multiple (LCM) of 173 and 113 is 19549.
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 173 and 113?
First, calculate the GCD of 173 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 113 = 1 remainder 60 |
| 2 | 113 ÷ 60 = 1 remainder 53 |
| 3 | 60 ÷ 53 = 1 remainder 7 |
| 4 | 53 ÷ 7 = 7 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 126 | 7686 |
| 170 and 40 | 680 |
| 129 and 53 | 6837 |
| 43 and 87 | 3741 |
| 133 and 12 | 1596 |