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 |
|---|---|
| 143 and 77 | 1001 |
| 193 and 13 | 2509 |
| 31 and 29 | 899 |
| 184 and 27 | 4968 |
| 191 and 12 | 2292 |