Least Common Multiple (LCM) of 23 and 63
The least common multiple (LCM) of 23 and 63 is 1449.
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 23 and 63?
First, calculate the GCD of 23 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 63 = 0 remainder 23 |
| 2 | 63 ÷ 23 = 2 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 |
|---|---|
| 135 and 28 | 3780 |
| 55 and 43 | 2365 |
| 117 and 159 | 6201 |
| 119 and 63 | 1071 |
| 85 and 62 | 5270 |