Least Common Multiple (LCM) of 168 and 110
The least common multiple (LCM) of 168 and 110 is 9240.
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 168 and 110?
First, calculate the GCD of 168 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 110 = 1 remainder 58 |
| 2 | 110 ÷ 58 = 1 remainder 52 |
| 3 | 58 ÷ 52 = 1 remainder 6 |
| 4 | 52 ÷ 6 = 8 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 51 | 5610 |
| 71 and 120 | 8520 |
| 178 and 51 | 9078 |
| 161 and 132 | 21252 |
| 177 and 21 | 1239 |