Least Common Multiple (LCM) of 31 and 35
The least common multiple (LCM) of 31 and 35 is 1085.
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 35?
First, calculate the GCD of 31 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 35 = 0 remainder 31 |
| 2 | 35 ÷ 31 = 1 remainder 4 |
| 3 | 31 ÷ 4 = 7 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 131 | 25283 |
| 165 and 154 | 2310 |
| 164 and 24 | 984 |
| 169 and 26 | 338 |
| 87 and 182 | 15834 |