Least Common Multiple (LCM) of 119 and 162
The least common multiple (LCM) of 119 and 162 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 119 and 162?
First, calculate the GCD of 119 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 162 = 0 remainder 119 |
| 2 | 162 ÷ 119 = 1 remainder 43 |
| 3 | 119 ÷ 43 = 2 remainder 33 |
| 4 | 43 ÷ 33 = 1 remainder 10 |
| 5 | 33 ÷ 10 = 3 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 42 | 1680 |
| 91 and 159 | 14469 |
| 27 and 83 | 2241 |
| 177 and 41 | 7257 |
| 105 and 58 | 6090 |