Least Common Multiple (LCM) of 95 and 112
The least common multiple (LCM) of 95 and 112 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 95 and 112?
First, calculate the GCD of 95 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 95 ÷ 112 = 0 remainder 95 |
| 2 | 112 ÷ 95 = 1 remainder 17 |
| 3 | 95 ÷ 17 = 5 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 170 | 30770 |
| 45 and 115 | 1035 |
| 165 and 129 | 7095 |
| 53 and 78 | 4134 |
| 188 and 104 | 4888 |