Least Common Multiple (LCM) of 112 and 77
The least common multiple (LCM) of 112 and 77 is 1232.
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 77?
First, calculate the GCD of 112 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 77 = 1 remainder 35 |
| 2 | 77 ÷ 35 = 2 remainder 7 |
| 3 | 35 ÷ 7 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 84 | 8988 |
| 98 and 152 | 7448 |
| 136 and 168 | 2856 |
| 100 and 17 | 1700 |
| 76 and 126 | 4788 |