Least Common Multiple (LCM) of 19 and 162
The least common multiple (LCM) of 19 and 162 is 3078.
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 19 and 162?
First, calculate the GCD of 19 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 162 = 0 remainder 19 |
| 2 | 162 ÷ 19 = 8 remainder 10 |
| 3 | 19 ÷ 10 = 1 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 23 | 3128 |
| 43 and 56 | 2408 |
| 110 and 190 | 2090 |
| 184 and 12 | 552 |
| 178 and 164 | 14596 |