Least Common Multiple (LCM) of 104 and 132
The least common multiple (LCM) of 104 and 132 is 3432.
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 104 and 132?
First, calculate the GCD of 104 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 132 = 0 remainder 104 |
| 2 | 132 ÷ 104 = 1 remainder 28 |
| 3 | 104 ÷ 28 = 3 remainder 20 |
| 4 | 28 ÷ 20 = 1 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 93 | 930 |
| 28 and 68 | 476 |
| 51 and 180 | 3060 |
| 70 and 96 | 3360 |
| 159 and 196 | 31164 |