Least Common Multiple (LCM) of 169 and 63
The least common multiple (LCM) of 169 and 63 is 10647.
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 169 and 63?
First, calculate the GCD of 169 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 63 = 2 remainder 43 |
| 2 | 63 ÷ 43 = 1 remainder 20 |
| 3 | 43 ÷ 20 = 2 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 99 | 2475 |
| 166 and 193 | 32038 |
| 126 and 151 | 19026 |
| 89 and 43 | 3827 |
| 100 and 78 | 3900 |