Least Common Multiple (LCM) of 105 and 51
The least common multiple (LCM) of 105 and 51 is 1785.
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 105 and 51?
First, calculate the GCD of 105 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 51 = 2 remainder 3 |
| 2 | 51 ÷ 3 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 199 | 21492 |
| 138 and 161 | 966 |
| 22 and 93 | 2046 |
| 138 and 78 | 1794 |
| 165 and 54 | 2970 |