Least Common Multiple (LCM) of 38 and 168
The least common multiple (LCM) of 38 and 168 is 3192.
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 38 and 168?
First, calculate the GCD of 38 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 168 = 0 remainder 38 |
| 2 | 168 ÷ 38 = 4 remainder 16 |
| 3 | 38 ÷ 16 = 2 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 133 | 18088 |
| 133 and 132 | 17556 |
| 75 and 14 | 1050 |
| 110 and 120 | 1320 |
| 135 and 138 | 6210 |