Least Common Multiple (LCM) of 106 and 96
The least common multiple (LCM) of 106 and 96 is 5088.
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 106 and 96?
First, calculate the GCD of 106 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 96 = 1 remainder 10 |
| 2 | 96 ÷ 10 = 9 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 90 | 270 |
| 76 and 174 | 6612 |
| 171 and 76 | 684 |
| 55 and 98 | 5390 |
| 52 and 19 | 988 |