Least Common Multiple (LCM) of 180 and 110
The least common multiple (LCM) of 180 and 110 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 180 and 110?
First, calculate the GCD of 180 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 110 = 1 remainder 70 |
| 2 | 110 ÷ 70 = 1 remainder 40 |
| 3 | 70 ÷ 40 = 1 remainder 30 |
| 4 | 40 ÷ 30 = 1 remainder 10 |
| 5 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 68 | 612 |
| 136 and 98 | 6664 |
| 38 and 197 | 7486 |
| 107 and 10 | 1070 |
| 118 and 177 | 354 |