Least Common Multiple (LCM) of 112 and 33
The least common multiple (LCM) of 112 and 33 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 33?
First, calculate the GCD of 112 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 33 = 3 remainder 13 |
| 2 | 33 ÷ 13 = 2 remainder 7 |
| 3 | 13 ÷ 7 = 1 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 157 | 25434 |
| 152 and 119 | 18088 |
| 192 and 16 | 192 |
| 183 and 51 | 3111 |
| 132 and 109 | 14388 |