Least Common Multiple (LCM) of 63 and 99
The least common multiple (LCM) of 63 and 99 is 693.
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 99?
First, calculate the GCD of 63 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 99 = 0 remainder 63 |
| 2 | 99 ÷ 63 = 1 remainder 36 |
| 3 | 63 ÷ 36 = 1 remainder 27 |
| 4 | 36 ÷ 27 = 1 remainder 9 |
| 5 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 111 | 1221 |
| 44 and 68 | 748 |
| 127 and 27 | 3429 |
| 23 and 78 | 1794 |
| 127 and 57 | 7239 |