Least Common Multiple (LCM) of 48 and 162
The least common multiple (LCM) of 48 and 162 is 1296.
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 48 and 162?
First, calculate the GCD of 48 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 162 = 0 remainder 48 |
| 2 | 162 ÷ 48 = 3 remainder 18 |
| 3 | 48 ÷ 18 = 2 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 57 | 798 |
| 145 and 31 | 4495 |
| 193 and 178 | 34354 |
| 43 and 55 | 2365 |
| 59 and 78 | 4602 |