Least Common Multiple (LCM) of 75 and 132
The least common multiple (LCM) of 75 and 132 is 3300.
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 132?
First, calculate the GCD of 75 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 132 = 0 remainder 75 |
| 2 | 132 ÷ 75 = 1 remainder 57 |
| 3 | 75 ÷ 57 = 1 remainder 18 |
| 4 | 57 ÷ 18 = 3 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 99 | 3465 |
| 123 and 31 | 3813 |
| 16 and 146 | 1168 |
| 155 and 138 | 21390 |
| 75 and 135 | 675 |