Least Common Multiple (LCM) of 63 and 105
The least common multiple (LCM) of 63 and 105 is 315.
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 105?
First, calculate the GCD of 63 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 105 = 0 remainder 63 |
| 2 | 105 ÷ 63 = 1 remainder 42 |
| 3 | 63 ÷ 42 = 1 remainder 21 |
| 4 | 42 ÷ 21 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 26 | 2132 |
| 80 and 83 | 6640 |
| 160 and 50 | 800 |
| 10 and 135 | 270 |
| 13 and 43 | 559 |