Least Common Multiple (LCM) of 176 and 49
The least common multiple (LCM) of 176 and 49 is 8624.
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 176 and 49?
First, calculate the GCD of 176 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 49 = 3 remainder 29 |
| 2 | 49 ÷ 29 = 1 remainder 20 |
| 3 | 29 ÷ 20 = 1 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 42 | 84 |
| 160 and 13 | 2080 |
| 179 and 78 | 13962 |
| 149 and 30 | 4470 |
| 72 and 173 | 12456 |