Least Common Multiple (LCM) of 112 and 95
The least common multiple (LCM) of 112 and 95 is 10640.
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 95?
First, calculate the GCD of 112 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 95 = 1 remainder 17 |
| 2 | 95 ÷ 17 = 5 remainder 10 |
| 3 | 17 ÷ 10 = 1 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 175 | 5425 |
| 49 and 161 | 1127 |
| 177 and 23 | 4071 |
| 170 and 13 | 2210 |
| 28 and 60 | 420 |