Least Common Multiple (LCM) of 168 and 30
The least common multiple (LCM) of 168 and 30 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 168 and 30?
First, calculate the GCD of 168 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 30 = 5 remainder 18 |
| 2 | 30 ÷ 18 = 1 remainder 12 |
| 3 | 18 ÷ 12 = 1 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 197 | 22852 |
| 14 and 77 | 154 |
| 16 and 40 | 80 |
| 188 and 59 | 11092 |
| 129 and 32 | 4128 |