Least Common Multiple (LCM) of 132 and 75
The least common multiple (LCM) of 132 and 75 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 132 and 75?
First, calculate the GCD of 132 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 75 = 1 remainder 57 |
| 2 | 75 ÷ 57 = 1 remainder 18 |
| 3 | 57 ÷ 18 = 3 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 119 | 3332 |
| 31 and 18 | 558 |
| 76 and 29 | 2204 |
| 187 and 146 | 27302 |
| 131 and 134 | 17554 |