Least Common Multiple (LCM) of 67 and 173
The least common multiple (LCM) of 67 and 173 is 11591.
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 67 and 173?
First, calculate the GCD of 67 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 173 = 0 remainder 67 |
| 2 | 173 ÷ 67 = 2 remainder 39 |
| 3 | 67 ÷ 39 = 1 remainder 28 |
| 4 | 39 ÷ 28 = 1 remainder 11 |
| 5 | 28 ÷ 11 = 2 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 41 | 3772 |
| 46 and 170 | 3910 |
| 37 and 10 | 370 |
| 77 and 132 | 924 |
| 111 and 109 | 12099 |