Least Common Multiple (LCM) of 96 and 49
The least common multiple (LCM) of 96 and 49 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 96 and 49?
First, calculate the GCD of 96 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 49 = 1 remainder 47 |
| 2 | 49 ÷ 47 = 1 remainder 2 |
| 3 | 47 ÷ 2 = 23 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 97 | 5141 |
| 129 and 69 | 2967 |
| 62 and 62 | 62 |
| 189 and 40 | 7560 |
| 94 and 199 | 18706 |