Least Common Multiple (LCM) of 96 and 146
The least common multiple (LCM) of 96 and 146 is 7008.
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 96 and 146?
First, calculate the GCD of 96 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 146 = 0 remainder 96 |
| 2 | 146 ÷ 96 = 1 remainder 50 |
| 3 | 96 ÷ 50 = 1 remainder 46 |
| 4 | 50 ÷ 46 = 1 remainder 4 |
| 5 | 46 ÷ 4 = 11 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 108 | 2160 |
| 109 and 107 | 11663 |
| 22 and 174 | 1914 |
| 142 and 71 | 142 |
| 41 and 48 | 1968 |