Least Common Multiple (LCM) of 63 and 164
The least common multiple (LCM) of 63 and 164 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 63 and 164?
First, calculate the GCD of 63 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 164 = 0 remainder 63 |
| 2 | 164 ÷ 63 = 2 remainder 38 |
| 3 | 63 ÷ 38 = 1 remainder 25 |
| 4 | 38 ÷ 25 = 1 remainder 13 |
| 5 | 25 ÷ 13 = 1 remainder 12 |
| 6 | 13 ÷ 12 = 1 remainder 1 |
| 7 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 164 | 10004 |
| 188 and 177 | 33276 |
| 113 and 86 | 9718 |
| 135 and 89 | 12015 |
| 172 and 148 | 6364 |