Least Common Multiple (LCM) of 31 and 63
The least common multiple (LCM) of 31 and 63 is 1953.
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 63?
First, calculate the GCD of 31 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 63 = 0 remainder 31 |
| 2 | 63 ÷ 31 = 2 remainder 1 |
| 3 | 31 ÷ 1 = 31 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 59 | 11387 |
| 105 and 117 | 4095 |
| 149 and 114 | 16986 |
| 123 and 47 | 5781 |
| 19 and 74 | 1406 |