Least Common Multiple (LCM) of 132 and 112
The least common multiple (LCM) of 132 and 112 is 3696.
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 112?
First, calculate the GCD of 132 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 112 = 1 remainder 20 |
| 2 | 112 ÷ 20 = 5 remainder 12 |
| 3 | 20 ÷ 12 = 1 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 86 | 5418 |
| 113 and 105 | 11865 |
| 57 and 187 | 10659 |
| 186 and 85 | 15810 |
| 171 and 87 | 4959 |