Least Common Multiple (LCM) of 55 and 63
The least common multiple (LCM) of 55 and 63 is 3465.
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 55 and 63?
First, calculate the GCD of 55 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 63 = 0 remainder 55 |
| 2 | 63 ÷ 55 = 1 remainder 8 |
| 3 | 55 ÷ 8 = 6 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 144 | 576 |
| 31 and 22 | 682 |
| 140 and 122 | 8540 |
| 187 and 11 | 187 |
| 112 and 44 | 1232 |