Least Common Multiple (LCM) of 167 and 63
The least common multiple (LCM) of 167 and 63 is 10521.
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 167 and 63?
First, calculate the GCD of 167 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 63 = 2 remainder 41 |
| 2 | 63 ÷ 41 = 1 remainder 22 |
| 3 | 41 ÷ 22 = 1 remainder 19 |
| 4 | 22 ÷ 19 = 1 remainder 3 |
| 5 | 19 ÷ 3 = 6 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 76 | 14668 |
| 167 and 42 | 7014 |
| 105 and 22 | 2310 |
| 10 and 144 | 720 |
| 14 and 200 | 1400 |