Least Common Multiple (LCM) of 105 and 88
The least common multiple (LCM) of 105 and 88 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 105 and 88?
First, calculate the GCD of 105 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 88 = 1 remainder 17 |
| 2 | 88 ÷ 17 = 5 remainder 3 |
| 3 | 17 ÷ 3 = 5 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 56 | 8904 |
| 189 and 198 | 4158 |
| 165 and 137 | 22605 |
| 46 and 103 | 4738 |
| 189 and 74 | 13986 |