Least Common Multiple (LCM) of 162 and 119
The least common multiple (LCM) of 162 and 119 is 19278.
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 119?
First, calculate the GCD of 162 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 119 = 1 remainder 43 |
| 2 | 119 ÷ 43 = 2 remainder 33 |
| 3 | 43 ÷ 33 = 1 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 123 | 6765 |
| 35 and 60 | 420 |
| 147 and 171 | 8379 |
| 16 and 52 | 208 |
| 19 and 188 | 3572 |