Least Common Multiple (LCM) of 112 and 76
The least common multiple (LCM) of 112 and 76 is 2128.
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 76?
First, calculate the GCD of 112 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 76 = 1 remainder 36 |
| 2 | 76 ÷ 36 = 2 remainder 4 |
| 3 | 36 ÷ 4 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 28 | 1708 |
| 30 and 159 | 1590 |
| 36 and 170 | 3060 |
| 18 and 12 | 36 |
| 114 and 133 | 798 |