Least Common Multiple (LCM) of 34 and 179
The least common multiple (LCM) of 34 and 179 is 6086.
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 34 and 179?
First, calculate the GCD of 34 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 179 = 0 remainder 34 |
| 2 | 179 ÷ 34 = 5 remainder 9 |
| 3 | 34 ÷ 9 = 3 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 72 | 144 |
| 172 and 176 | 7568 |
| 126 and 183 | 7686 |
| 10 and 126 | 630 |
| 43 and 24 | 1032 |