Least Common Multiple (LCM) of 142 and 173
The least common multiple (LCM) of 142 and 173 is 24566.
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 142 and 173?
First, calculate the GCD of 142 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 173 = 0 remainder 142 |
| 2 | 173 ÷ 142 = 1 remainder 31 |
| 3 | 142 ÷ 31 = 4 remainder 18 |
| 4 | 31 ÷ 18 = 1 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 110 | 10230 |
| 38 and 65 | 2470 |
| 64 and 119 | 7616 |
| 196 and 14 | 196 |
| 185 and 106 | 19610 |