Least Common Multiple (LCM) of 113 and 173
The least common multiple (LCM) of 113 and 173 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 113 and 173?
First, calculate the GCD of 113 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 173 = 0 remainder 113 |
| 2 | 173 ÷ 113 = 1 remainder 60 |
| 3 | 113 ÷ 60 = 1 remainder 53 |
| 4 | 60 ÷ 53 = 1 remainder 7 |
| 5 | 53 ÷ 7 = 7 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 90 | 1440 |
| 144 and 80 | 720 |
| 196 and 155 | 30380 |
| 72 and 114 | 1368 |
| 71 and 146 | 10366 |