Least Common Multiple (LCM) of 162 and 105
The least common multiple (LCM) of 162 and 105 is 5670.
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 105?
First, calculate the GCD of 162 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 105 = 1 remainder 57 |
| 2 | 105 ÷ 57 = 1 remainder 48 |
| 3 | 57 ÷ 48 = 1 remainder 9 |
| 4 | 48 ÷ 9 = 5 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 36 | 5220 |
| 112 and 74 | 4144 |
| 126 and 75 | 3150 |
| 40 and 88 | 440 |
| 68 and 47 | 3196 |