Least Common Multiple (LCM) of 105 and 180
The least common multiple (LCM) of 105 and 180 is 1260.
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 105 and 180?
First, calculate the GCD of 105 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 180 = 0 remainder 105 |
| 2 | 180 ÷ 105 = 1 remainder 75 |
| 3 | 105 ÷ 75 = 1 remainder 30 |
| 4 | 75 ÷ 30 = 2 remainder 15 |
| 5 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 80 | 880 |
| 61 and 122 | 122 |
| 150 and 29 | 4350 |
| 120 and 131 | 15720 |
| 29 and 63 | 1827 |