Least Common Multiple (LCM) of 51 and 110
The least common multiple (LCM) of 51 and 110 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 51 and 110?
First, calculate the GCD of 51 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 110 = 0 remainder 51 |
| 2 | 110 ÷ 51 = 2 remainder 8 |
| 3 | 51 ÷ 8 = 6 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 149 | 25181 |
| 164 and 159 | 26076 |
| 99 and 142 | 14058 |
| 136 and 139 | 18904 |
| 54 and 109 | 5886 |