Least Common Multiple (LCM) of 49 and 176
The least common multiple (LCM) of 49 and 176 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 49 and 176?
First, calculate the GCD of 49 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 176 = 0 remainder 49 |
| 2 | 176 ÷ 49 = 3 remainder 29 |
| 3 | 49 ÷ 29 = 1 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 84 | 9156 |
| 199 and 135 | 26865 |
| 13 and 42 | 546 |
| 71 and 62 | 4402 |
| 109 and 112 | 12208 |