Least Common Multiple (LCM) of 112 and 79
The least common multiple (LCM) of 112 and 79 is 8848.
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 79?
First, calculate the GCD of 112 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 79 = 1 remainder 33 |
| 2 | 79 ÷ 33 = 2 remainder 13 |
| 3 | 33 ÷ 13 = 2 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 90 | 1440 |
| 38 and 121 | 4598 |
| 15 and 147 | 735 |
| 109 and 119 | 12971 |
| 119 and 31 | 3689 |