Least Common Multiple (LCM) of 63 and 106
The least common multiple (LCM) of 63 and 106 is 6678.
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 106?
First, calculate the GCD of 63 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 106 = 0 remainder 63 |
| 2 | 106 ÷ 63 = 1 remainder 43 |
| 3 | 63 ÷ 43 = 1 remainder 20 |
| 4 | 43 ÷ 20 = 2 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 128 | 1920 |
| 114 and 185 | 21090 |
| 150 and 45 | 450 |
| 34 and 161 | 5474 |
| 186 and 36 | 1116 |