Least Common Multiple (LCM) of 12 and 173
The least common multiple (LCM) of 12 and 173 is 2076.
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 12 and 173?
First, calculate the GCD of 12 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 173 = 0 remainder 12 |
| 2 | 173 ÷ 12 = 14 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 101 | 6767 |
| 113 and 64 | 7232 |
| 29 and 45 | 1305 |
| 68 and 63 | 4284 |
| 146 and 16 | 1168 |