Least Common Multiple (LCM) of 163 and 67
The least common multiple (LCM) of 163 and 67 is 10921.
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 163 and 67?
First, calculate the GCD of 163 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 67 = 2 remainder 29 |
| 2 | 67 ÷ 29 = 2 remainder 9 |
| 3 | 29 ÷ 9 = 3 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 119 | 6307 |
| 144 and 118 | 8496 |
| 133 and 189 | 3591 |
| 115 and 31 | 3565 |
| 65 and 74 | 4810 |