Least Common Multiple (LCM) of 180 and 46
The least common multiple (LCM) of 180 and 46 is 4140.
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 46?
First, calculate the GCD of 180 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 46 = 3 remainder 42 |
| 2 | 46 ÷ 42 = 1 remainder 4 |
| 3 | 42 ÷ 4 = 10 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 86 | 8514 |
| 193 and 44 | 8492 |
| 194 and 91 | 17654 |
| 120 and 17 | 2040 |
| 90 and 84 | 1260 |