Least Common Multiple (LCM) of 63 and 111
The least common multiple (LCM) of 63 and 111 is 2331.
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 111?
First, calculate the GCD of 63 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 111 = 0 remainder 63 |
| 2 | 111 ÷ 63 = 1 remainder 48 |
| 3 | 63 ÷ 48 = 1 remainder 15 |
| 4 | 48 ÷ 15 = 3 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 165 | 25905 |
| 33 and 98 | 3234 |
| 196 and 34 | 3332 |
| 39 and 188 | 7332 |
| 193 and 36 | 6948 |