Least Common Multiple (LCM) of 75 and 52
The least common multiple (LCM) of 75 and 52 is 3900.
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 52?
First, calculate the GCD of 75 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 52 = 1 remainder 23 |
| 2 | 52 ÷ 23 = 2 remainder 6 |
| 3 | 23 ÷ 6 = 3 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 110 | 1760 |
| 81 and 49 | 3969 |
| 99 and 89 | 8811 |
| 193 and 198 | 38214 |
| 155 and 116 | 17980 |