Least Common Multiple (LCM) of 31 and 174
The least common multiple (LCM) of 31 and 174 is 5394.
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 174?
First, calculate the GCD of 31 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 174 = 0 remainder 31 |
| 2 | 174 ÷ 31 = 5 remainder 19 |
| 3 | 31 ÷ 19 = 1 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 96 | 5856 |
| 128 and 163 | 20864 |
| 152 and 113 | 17176 |
| 112 and 132 | 3696 |
| 170 and 31 | 5270 |