Least Common Multiple (LCM) of 180 and 143
The least common multiple (LCM) of 180 and 143 is 25740.
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 143?
First, calculate the GCD of 180 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 143 = 1 remainder 37 |
| 2 | 143 ÷ 37 = 3 remainder 32 |
| 3 | 37 ÷ 32 = 1 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 64 | 1472 |
| 176 and 176 | 176 |
| 100 and 49 | 4900 |
| 73 and 47 | 3431 |
| 15 and 196 | 2940 |