Least Common Multiple (LCM) of 42 and 96
The least common multiple (LCM) of 42 and 96 is 672.
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 42 and 96?
First, calculate the GCD of 42 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 96 = 0 remainder 42 |
| 2 | 96 ÷ 42 = 2 remainder 12 |
| 3 | 42 ÷ 12 = 3 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 24 | 120 |
| 47 and 59 | 2773 |
| 135 and 132 | 5940 |
| 140 and 82 | 5740 |
| 135 and 186 | 8370 |