Least Common Multiple (LCM) of 75 and 99
The least common multiple (LCM) of 75 and 99 is 2475.
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 99?
First, calculate the GCD of 75 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 99 = 0 remainder 75 |
| 2 | 99 ÷ 75 = 1 remainder 24 |
| 3 | 75 ÷ 24 = 3 remainder 3 |
| 4 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 65 | 9360 |
| 118 and 184 | 10856 |
| 196 and 171 | 33516 |
| 44 and 37 | 1628 |
| 49 and 175 | 1225 |