Least Common Multiple (LCM) of 48 and 112
The least common multiple (LCM) of 48 and 112 is 336.
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 48 and 112?
First, calculate the GCD of 48 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 112 = 0 remainder 48 |
| 2 | 112 ÷ 48 = 2 remainder 16 |
| 3 | 48 ÷ 16 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 129 | 6192 |
| 110 and 90 | 990 |
| 82 and 19 | 1558 |
| 116 and 108 | 3132 |
| 122 and 157 | 19154 |