Least Common Multiple (LCM) of 30 and 173
The least common multiple (LCM) of 30 and 173 is 5190.
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 30 and 173?
First, calculate the GCD of 30 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 173 = 0 remainder 30 |
| 2 | 173 ÷ 30 = 5 remainder 23 |
| 3 | 30 ÷ 23 = 1 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 74 | 13098 |
| 79 and 64 | 5056 |
| 113 and 106 | 11978 |
| 162 and 129 | 6966 |
| 12 and 105 | 420 |