Least Common Multiple (LCM) of 23 and 132
The least common multiple (LCM) of 23 and 132 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 23 and 132?
First, calculate the GCD of 23 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 132 = 0 remainder 23 |
| 2 | 132 ÷ 23 = 5 remainder 17 |
| 3 | 23 ÷ 17 = 1 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 65 | 9035 |
| 75 and 55 | 825 |
| 175 and 54 | 9450 |
| 170 and 48 | 4080 |
| 181 and 106 | 19186 |