Least Common Multiple (LCM) of 112 and 132
The least common multiple (LCM) of 112 and 132 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 112 and 132?
First, calculate the GCD of 112 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 132 = 0 remainder 112 |
| 2 | 132 ÷ 112 = 1 remainder 20 |
| 3 | 112 ÷ 20 = 5 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 164 | 11316 |
| 195 and 49 | 9555 |
| 120 and 21 | 840 |
| 96 and 140 | 3360 |
| 39 and 195 | 195 |