Least Common Multiple (LCM) of 132 and 23
The least common multiple (LCM) of 132 and 23 is 3036.
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 23?
First, calculate the GCD of 132 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 23 = 5 remainder 17 |
| 2 | 23 ÷ 17 = 1 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 74 | 74 |
| 60 and 100 | 300 |
| 110 and 100 | 1100 |
| 154 and 53 | 8162 |
| 87 and 56 | 4872 |