Least Common Multiple (LCM) of 14 and 162
The least common multiple (LCM) of 14 and 162 is 1134.
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 14 and 162?
First, calculate the GCD of 14 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 162 = 0 remainder 14 |
| 2 | 162 ÷ 14 = 11 remainder 8 |
| 3 | 14 ÷ 8 = 1 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 111 | 11211 |
| 70 and 79 | 5530 |
| 35 and 119 | 595 |
| 14 and 119 | 238 |
| 130 and 131 | 17030 |