Least Common Multiple (LCM) of 52 and 75
The least common multiple (LCM) of 52 and 75 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 52 and 75?
First, calculate the GCD of 52 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 75 = 0 remainder 52 |
| 2 | 75 ÷ 52 = 1 remainder 23 |
| 3 | 52 ÷ 23 = 2 remainder 6 |
| 4 | 23 ÷ 6 = 3 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 26 | 1846 |
| 103 and 31 | 3193 |
| 24 and 85 | 2040 |
| 30 and 155 | 930 |
| 61 and 110 | 6710 |