Least Common Multiple (LCM) of 40 and 63
The least common multiple (LCM) of 40 and 63 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 40 and 63?
First, calculate the GCD of 40 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 63 = 0 remainder 40 |
| 2 | 63 ÷ 40 = 1 remainder 23 |
| 3 | 40 ÷ 23 = 1 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 55 | 9790 |
| 165 and 96 | 5280 |
| 172 and 75 | 12900 |
| 38 and 112 | 2128 |
| 34 and 96 | 1632 |