Least Common Multiple (LCM) of 32 and 75
The least common multiple (LCM) of 32 and 75 is 2400.
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 32 and 75?
First, calculate the GCD of 32 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 75 = 0 remainder 32 |
| 2 | 75 ÷ 32 = 2 remainder 11 |
| 3 | 32 ÷ 11 = 2 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 170 | 1530 |
| 148 and 132 | 4884 |
| 163 and 104 | 16952 |
| 124 and 156 | 4836 |
| 110 and 135 | 2970 |