Least Common Multiple (LCM) of 112 and 69
The least common multiple (LCM) of 112 and 69 is 7728.
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 69?
First, calculate the GCD of 112 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 69 = 1 remainder 43 |
| 2 | 69 ÷ 43 = 1 remainder 26 |
| 3 | 43 ÷ 26 = 1 remainder 17 |
| 4 | 26 ÷ 17 = 1 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 84 | 1260 |
| 64 and 11 | 704 |
| 151 and 115 | 17365 |
| 60 and 58 | 1740 |
| 44 and 77 | 308 |