Least Common Multiple (LCM) of 63 and 110
The least common multiple (LCM) of 63 and 110 is 6930.
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 110?
First, calculate the GCD of 63 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 110 = 0 remainder 63 |
| 2 | 110 ÷ 63 = 1 remainder 47 |
| 3 | 63 ÷ 47 = 1 remainder 16 |
| 4 | 47 ÷ 16 = 2 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 28 | 308 |
| 151 and 74 | 11174 |
| 24 and 57 | 456 |
| 152 and 65 | 9880 |
| 195 and 41 | 7995 |