Least Common Multiple (LCM) of 63 and 96
The least common multiple (LCM) of 63 and 96 is 2016.
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 63 and 96?
First, calculate the GCD of 63 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 96 = 0 remainder 63 |
| 2 | 96 ÷ 63 = 1 remainder 33 |
| 3 | 63 ÷ 33 = 1 remainder 30 |
| 4 | 33 ÷ 30 = 1 remainder 3 |
| 5 | 30 ÷ 3 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 28 | 2436 |
| 120 and 135 | 1080 |
| 100 and 136 | 3400 |
| 119 and 131 | 15589 |
| 123 and 186 | 7626 |