Least Common Multiple (LCM) of 42 and 31
The least common multiple (LCM) of 42 and 31 is 1302.
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 42 and 31?
First, calculate the GCD of 42 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 31 = 1 remainder 11 |
| 2 | 31 ÷ 11 = 2 remainder 9 |
| 3 | 11 ÷ 9 = 1 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 146 | 2190 |
| 59 and 162 | 9558 |
| 165 and 16 | 2640 |
| 110 and 86 | 4730 |
| 130 and 47 | 6110 |