Least Common Multiple (LCM) of 96 and 140
The least common multiple (LCM) of 96 and 140 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 96 and 140?
First, calculate the GCD of 96 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 140 = 0 remainder 96 |
| 2 | 140 ÷ 96 = 1 remainder 44 |
| 3 | 96 ÷ 44 = 2 remainder 8 |
| 4 | 44 ÷ 8 = 5 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 78 | 12714 |
| 112 and 174 | 9744 |
| 99 and 124 | 12276 |
| 25 and 108 | 2700 |
| 33 and 49 | 1617 |