Least Common Multiple (LCM) of 132 and 30
The least common multiple (LCM) of 132 and 30 is 660.
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 30?
First, calculate the GCD of 132 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 30 = 4 remainder 12 |
| 2 | 30 ÷ 12 = 2 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 57 | 2679 |
| 53 and 75 | 3975 |
| 14 and 67 | 938 |
| 118 and 108 | 6372 |
| 54 and 34 | 918 |