Least Common Multiple (LCM) of 31 and 162
The least common multiple (LCM) of 31 and 162 is 5022.
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 162?
First, calculate the GCD of 31 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 162 = 0 remainder 31 |
| 2 | 162 ÷ 31 = 5 remainder 7 |
| 3 | 31 ÷ 7 = 4 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 74 | 3034 |
| 193 and 103 | 19879 |
| 50 and 93 | 4650 |
| 125 and 161 | 20125 |
| 32 and 87 | 2784 |