Least Common Multiple (LCM) of 49 and 96
The least common multiple (LCM) of 49 and 96 is 4704.
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 49 and 96?
First, calculate the GCD of 49 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 96 = 0 remainder 49 |
| 2 | 96 ÷ 49 = 1 remainder 47 |
| 3 | 49 ÷ 47 = 1 remainder 2 |
| 4 | 47 ÷ 2 = 23 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 160 | 13280 |
| 38 and 193 | 7334 |
| 96 and 107 | 10272 |
| 96 and 126 | 2016 |
| 145 and 184 | 26680 |