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 |
|---|---|
| 162 and 160 | 12960 |
| 128 and 135 | 17280 |
| 76 and 197 | 14972 |
| 106 and 14 | 742 |
| 79 and 129 | 10191 |