Least Common Multiple (LCM) of 110 and 114
The least common multiple (LCM) of 110 and 114 is 6270.
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 114?
First, calculate the GCD of 110 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 114 = 0 remainder 110 |
| 2 | 114 ÷ 110 = 1 remainder 4 |
| 3 | 110 ÷ 4 = 27 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 113 | 15255 |
| 169 and 147 | 24843 |
| 108 and 99 | 1188 |
| 16 and 179 | 2864 |
| 57 and 89 | 5073 |