Least Common Multiple (LCM) of 164 and 63
The least common multiple (LCM) of 164 and 63 is 10332.
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 164 and 63?
First, calculate the GCD of 164 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 63 = 2 remainder 38 |
| 2 | 63 ÷ 38 = 1 remainder 25 |
| 3 | 38 ÷ 25 = 1 remainder 13 |
| 4 | 25 ÷ 13 = 1 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 27 | 3051 |
| 43 and 170 | 7310 |
| 163 and 34 | 5542 |
| 199 and 103 | 20497 |
| 171 and 146 | 24966 |