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 |
|---|---|
| 154 and 183 | 28182 |
| 44 and 178 | 3916 |
| 169 and 22 | 3718 |
| 164 and 117 | 19188 |
| 96 and 112 | 672 |