Least Common Multiple (LCM) of 63 and 40
The least common multiple (LCM) of 63 and 40 is 2520.
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 40?
First, calculate the GCD of 63 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 40 = 1 remainder 23 |
| 2 | 40 ÷ 23 = 1 remainder 17 |
| 3 | 23 ÷ 17 = 1 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 200 | 7800 |
| 90 and 34 | 1530 |
| 23 and 92 | 92 |
| 97 and 78 | 7566 |
| 105 and 60 | 420 |