Least Common Multiple (LCM) of 162 and 104
The least common multiple (LCM) of 162 and 104 is 8424.
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 104?
First, calculate the GCD of 162 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 104 = 1 remainder 58 |
| 2 | 104 ÷ 58 = 1 remainder 46 |
| 3 | 58 ÷ 46 = 1 remainder 12 |
| 4 | 46 ÷ 12 = 3 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 112 | 2800 |
| 184 and 40 | 920 |
| 173 and 198 | 34254 |
| 17 and 139 | 2363 |
| 196 and 120 | 5880 |