Least Common Multiple (LCM) of 34 and 176
The least common multiple (LCM) of 34 and 176 is 2992.
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 176?
First, calculate the GCD of 34 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 176 = 0 remainder 34 |
| 2 | 176 ÷ 34 = 5 remainder 6 |
| 3 | 34 ÷ 6 = 5 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 130 | 3250 |
| 180 and 72 | 360 |
| 41 and 10 | 410 |
| 38 and 156 | 2964 |
| 82 and 172 | 7052 |