Least Common Multiple (LCM) of 35 and 96
The least common multiple (LCM) of 35 and 96 is 3360.
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 35 and 96?
First, calculate the GCD of 35 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 96 = 0 remainder 35 |
| 2 | 96 ÷ 35 = 2 remainder 26 |
| 3 | 35 ÷ 26 = 1 remainder 9 |
| 4 | 26 ÷ 9 = 2 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 181 | 3258 |
| 94 and 49 | 4606 |
| 156 and 67 | 10452 |
| 70 and 81 | 5670 |
| 71 and 140 | 9940 |