Least Common Multiple (LCM) of 110 and 51
The least common multiple (LCM) of 110 and 51 is 5610.
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 51?
First, calculate the GCD of 110 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 51 = 2 remainder 8 |
| 2 | 51 ÷ 8 = 6 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 121 | 15246 |
| 146 and 156 | 11388 |
| 53 and 40 | 2120 |
| 190 and 119 | 22610 |
| 144 and 199 | 28656 |