Least Common Multiple (LCM) of 30 and 168
The least common multiple (LCM) of 30 and 168 is 840.
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 30 and 168?
First, calculate the GCD of 30 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 168 = 0 remainder 30 |
| 2 | 168 ÷ 30 = 5 remainder 18 |
| 3 | 30 ÷ 18 = 1 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 132 | 1980 |
| 100 and 57 | 5700 |
| 185 and 162 | 29970 |
| 31 and 48 | 1488 |
| 101 and 34 | 3434 |