Least Common Multiple (LCM) of 31 and 168
The least common multiple (LCM) of 31 and 168 is 5208.
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 31 and 168?
First, calculate the GCD of 31 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 168 = 0 remainder 31 |
| 2 | 168 ÷ 31 = 5 remainder 13 |
| 3 | 31 ÷ 13 = 2 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 91 | 6916 |
| 162 and 35 | 5670 |
| 142 and 15 | 2130 |
| 196 and 44 | 2156 |
| 168 and 163 | 27384 |