Least Common Multiple (LCM) of 177 and 49
The least common multiple (LCM) of 177 and 49 is 8673.
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 177 and 49?
First, calculate the GCD of 177 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 49 = 3 remainder 30 |
| 2 | 49 ÷ 30 = 1 remainder 19 |
| 3 | 30 ÷ 19 = 1 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 120 | 12360 |
| 168 and 80 | 1680 |
| 156 and 119 | 18564 |
| 200 and 80 | 400 |
| 30 and 120 | 120 |