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 |
|---|---|
| 80 and 56 | 560 |
| 198 and 30 | 990 |
| 157 and 85 | 13345 |
| 150 and 64 | 4800 |
| 10 and 120 | 120 |