Least Common Multiple (LCM) of 67 and 162
The least common multiple (LCM) of 67 and 162 is 10854.
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 67 and 162?
First, calculate the GCD of 67 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 162 = 0 remainder 67 |
| 2 | 162 ÷ 67 = 2 remainder 28 |
| 3 | 67 ÷ 28 = 2 remainder 11 |
| 4 | 28 ÷ 11 = 2 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 33 | 957 |
| 107 and 78 | 8346 |
| 133 and 21 | 399 |
| 147 and 185 | 27195 |
| 76 and 193 | 14668 |