Least Common Multiple (LCM) of 49 and 180
The least common multiple (LCM) of 49 and 180 is 8820.
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 180?
First, calculate the GCD of 49 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 180 = 0 remainder 49 |
| 2 | 180 ÷ 49 = 3 remainder 33 |
| 3 | 49 ÷ 33 = 1 remainder 16 |
| 4 | 33 ÷ 16 = 2 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 152 | 4712 |
| 65 and 129 | 8385 |
| 82 and 113 | 9266 |
| 67 and 133 | 8911 |
| 43 and 162 | 6966 |