Least Common Multiple (LCM) of 105 and 112
The least common multiple (LCM) of 105 and 112 is 1680.
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 105 and 112?
First, calculate the GCD of 105 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 112 = 0 remainder 105 |
| 2 | 112 ÷ 105 = 1 remainder 7 |
| 3 | 105 ÷ 7 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 104 | 8424 |
| 72 and 105 | 2520 |
| 74 and 64 | 2368 |
| 32 and 41 | 1312 |
| 46 and 38 | 874 |