Least Common Multiple (LCM) of 75 and 11
The least common multiple (LCM) of 75 and 11 is 825.
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 75 and 11?
First, calculate the GCD of 75 and 11 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 11 = 6 remainder 9 |
| 2 | 11 ÷ 9 = 1 remainder 2 |
| 3 | 9 ÷ 2 = 4 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 19 | 228 |
| 113 and 24 | 2712 |
| 83 and 99 | 8217 |
| 119 and 183 | 21777 |
| 38 and 43 | 1634 |