Least Common Multiple (LCM) of 180 and 49
The least common multiple (LCM) of 180 and 49 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 180 and 49?
First, calculate the GCD of 180 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 49 = 3 remainder 33 |
| 2 | 49 ÷ 33 = 1 remainder 16 |
| 3 | 33 ÷ 16 = 2 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 166 | 6806 |
| 70 and 42 | 210 |
| 32 and 187 | 5984 |
| 142 and 82 | 5822 |
| 50 and 12 | 300 |