Least Common Multiple (LCM) of 162 and 91
The least common multiple (LCM) of 162 and 91 is 14742.
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 162 and 91?
First, calculate the GCD of 162 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 91 = 1 remainder 71 |
| 2 | 91 ÷ 71 = 1 remainder 20 |
| 3 | 71 ÷ 20 = 3 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 36 | 2412 |
| 187 and 90 | 16830 |
| 22 and 168 | 1848 |
| 56 and 16 | 112 |
| 145 and 123 | 17835 |