Least Common Multiple (LCM) of 31 and 70
The least common multiple (LCM) of 31 and 70 is 2170.
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 70?
First, calculate the GCD of 31 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 70 = 0 remainder 31 |
| 2 | 70 ÷ 31 = 2 remainder 8 |
| 3 | 31 ÷ 8 = 3 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 77 | 14476 |
| 18 and 185 | 3330 |
| 27 and 103 | 2781 |
| 182 and 134 | 12194 |
| 101 and 55 | 5555 |