Least Common Multiple (LCM) of 110 and 180
The least common multiple (LCM) of 110 and 180 is 1980.
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 110 and 180?
First, calculate the GCD of 110 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 180 = 0 remainder 110 |
| 2 | 180 ÷ 110 = 1 remainder 70 |
| 3 | 110 ÷ 70 = 1 remainder 40 |
| 4 | 70 ÷ 40 = 1 remainder 30 |
| 5 | 40 ÷ 30 = 1 remainder 10 |
| 6 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 52 | 1612 |
| 124 and 145 | 17980 |
| 96 and 49 | 4704 |
| 48 and 51 | 816 |
| 105 and 134 | 14070 |