Least Common Multiple (LCM) of 31 and 175
The least common multiple (LCM) of 31 and 175 is 5425.
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 175?
First, calculate the GCD of 31 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 175 = 0 remainder 31 |
| 2 | 175 ÷ 31 = 5 remainder 20 |
| 3 | 31 ÷ 20 = 1 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 85 | 16320 |
| 143 and 109 | 15587 |
| 87 and 149 | 12963 |
| 193 and 101 | 19493 |
| 120 and 115 | 2760 |