Least Common Multiple (LCM) of 140 and 96
The least common multiple (LCM) of 140 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 140 and 96?
First, calculate the GCD of 140 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 96 = 1 remainder 44 |
| 2 | 96 ÷ 44 = 2 remainder 8 |
| 3 | 44 ÷ 8 = 5 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 142 | 7242 |
| 162 and 67 | 10854 |
| 175 and 159 | 27825 |
| 145 and 42 | 6090 |
| 160 and 63 | 10080 |