Least Common Multiple (LCM) of 180 and 53
The least common multiple (LCM) of 180 and 53 is 9540.
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 53?
First, calculate the GCD of 180 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 53 = 3 remainder 21 |
| 2 | 53 ÷ 21 = 2 remainder 11 |
| 3 | 21 ÷ 11 = 1 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 124 | 1364 |
| 28 and 19 | 532 |
| 47 and 198 | 9306 |
| 104 and 131 | 13624 |
| 18 and 131 | 2358 |