Least Common Multiple (LCM) of 73 and 180
The least common multiple (LCM) of 73 and 180 is 13140.
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 73 and 180?
First, calculate the GCD of 73 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 180 = 0 remainder 73 |
| 2 | 180 ÷ 73 = 2 remainder 34 |
| 3 | 73 ÷ 34 = 2 remainder 5 |
| 4 | 34 ÷ 5 = 6 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 74 | 12950 |
| 89 and 105 | 9345 |
| 196 and 118 | 11564 |
| 173 and 140 | 24220 |
| 87 and 193 | 16791 |