Least Common Multiple (LCM) of 112 and 135
The least common multiple (LCM) of 112 and 135 is 15120.
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 135?
First, calculate the GCD of 112 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 135 = 0 remainder 112 |
| 2 | 135 ÷ 112 = 1 remainder 23 |
| 3 | 112 ÷ 23 = 4 remainder 20 |
| 4 | 23 ÷ 20 = 1 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 42 | 2562 |
| 192 and 54 | 1728 |
| 97 and 133 | 12901 |
| 187 and 161 | 30107 |
| 115 and 42 | 4830 |