Least Common Multiple (LCM) of 45 and 132
The least common multiple (LCM) of 45 and 132 is 1980.
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 45 and 132?
First, calculate the GCD of 45 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 132 = 0 remainder 45 |
| 2 | 132 ÷ 45 = 2 remainder 42 |
| 3 | 45 ÷ 42 = 1 remainder 3 |
| 4 | 42 ÷ 3 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 154 | 13860 |
| 110 and 88 | 440 |
| 108 and 158 | 8532 |
| 67 and 87 | 5829 |
| 41 and 85 | 3485 |